Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 236217

find the vertex, the line of symmetry and the maximum or minimum value of f(x). Graph the function f(x)=1/2(x+6)^2+3

Found 2 solutions by Edwin McCravy, stanbon:

Answer by Edwin McCravy(2878)

(Show Source):

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The equation



  



is 



a parabola with a vertex at (h,k) and which passes

through the points (h+1,k+a) and (h-1,k+a), and its

axis of symmetry is the vertical line whose equation

is 



So in the problem:







, , 



[Notice that the sign is changed for h but kept for k]



So the vertex is (h,k) or (-6,3),



The parabola passes through (h-1,k+a) and (h+1,k+a), or



(-6-1,3+) or (-7,) and



(-6+1,3+) or (-5,)



Its axis of symmetry is the vertical line whose equation



is  or 



We plot the vertex (-6,3)







We draw the axis of symmetry which is a vertical line 

through the vertex (the green line below:







Then we plot the two points, 

one on each side of the vertex



(-7,) and (-5,)











Finally we sketch in the parabola:







Edwin

Answer by stanbon(25959)   (Show Source):
You can put this solution on YOUR website!
find the vertex, the line of symmetry and the maximum or minimum value of f(x). Graph the function f(x)=1/2(x+6)^2+3
------------------
Vertex (-6,3)
Line of symmetry: x = -6
Minimum at the vertex is f(x)=3
-----------------------

=====================================================
Cheers,
Stan H.

Question 236220: use quadractic equation to find the x intercept if any. then evaluate the function for several values of x. f(x)=-x^2-2x-1
Answer by checkley77(6671)   (Show Source):
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f(x)=-x^2-2x-1
(graph 300x200 pixels, x from -6 to 5, y from -10 to 10, -x^2 -2x -1).
The x intercept=-1 & there are no other x intercepts.
y=-x^2-2x-1
Let x=2
y=-2^2-2*2-1
y=-4-4-1
y=-9 or (2,-9)
Let x=-4
y=-4^2-2*-4-1
y=-16+8-1
y=-9 or (-4,-9)

Question 236208: 4y^2-7y-15=0
Answer by jim_thompson5910(13679)   (Show Source):
You can put this solution on YOUR website!

Start with the given equation.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "y":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the solutions are or

Question 236187: x^-x=1 what is the solution set{ }?
quadratic formula.
Answer by jim_thompson5910(13679)   (Show Source):
You can put this solution on YOUR website!

Start with the given equation.

Subtract 1 from both sides.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

or Break up the expression.

So the solutions are or

which approximate to or

Question 236058: If the two solutions of a quadratic equation =-4 and 3 and c=4 then how do I solve this problem and write it in standard form?
Answer by Theo(548)   (Show Source):
You can put this solution on YOUR website!
If the roots are x = -4 and x = 3, then the equation would be:

(x+4) * (x-3) = 0

Multiply these factors together to get:

x^2 + x - 12 = 0

Since your c factor has to be 4, then you need to divide both sides of this equation by -3 to get:

-x^2/3 - x/3 + 4 = 0

This would be the same as:

-(1/3)*x^2 - (1/3)*x + 4 = 0

a would be equal to -(1/3)
b would be equal to -(1/3)
c would be equal to 4

If you were given this equation in this form to start with and asked to solve for the roots, you would have done the following:

Multiply both sides of the equation by (-3) to get:

x^2 + x - 12 = 0

Factor this equation to get:

(x-3) * (x+4) = 0

Solve for x to get:

x = 3
or:
x = -4

which is where you started from.

Question 236111: what are the two binomial factors of 6s^2+40s-64
Answer by stanbon(25959)   (Show Source):
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what are the two binomial factors of 6s^2+40s-64
--------
= 2(3s^2+20s-32)
---
Think of two numbers whose product is -32*3 = -96
and whose sum is 20.
The numbers are 24 and -4
Rewrite the problem:
= 2(3s^2+24s-4s-32)
Factor the 1st two and the last two terms of
the quadratic separately.
=2(3s^2+24s-4s-32)
=2(3s(s+8)-4(s+8))
Factor again to get:
---
= 2(3s-4)(s+8)
====================
Cheers,
Stan H.
===================

Question 236090: I must use the discriminant to determine the number of solutions of the quadratic equation and whether the solutions are real or complex. I am having trouble understanding how to find the discriminant and then find the solutions.
I do not need to find the roots.
3z^2 + z - 1 = 0
Answer by philline_palana(8)   (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=13 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.434258545910665, -0.767591879243998. Here's your graph:

Question 236062: solve showing and explaining all steps using quadractic formula,
x^2+2x-8=0
Answer by jim_thompson5910(13679)   (Show Source):
You can put this solution on YOUR website!

Start with the given equation.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the solutions are or

Question 236052: A student makes a $10.25 purchase at the bookstore with a $20 bill. The store has no bills and gives the change in quarters and fifty-cent pieces. there are 30 coins in all. how many of each kind are there?
Answer by checkley77(6671)   (Show Source):
You can put this solution on YOUR website!
Q+H=30 OR Q=30-H
.25Q+.50H=20-10.25
.25(30-H)+.50H=9.75
7.5-.25H+.50H=9.75
.25H=9.75-7.50
.25H=2.25
H=2.25/.25
H=9 HALF DOLLARS WERE PART OF THE CHANGE.
Q=30-9=21 QUARTERS WERE PART OF THE CHANGE.
PROOF:
.25*21+.50*9=9.75
5.25+4.50=9.75
9.75=9.75

Question 236057: factor
Answer by checkley77(6671)   (Show Source):
You can put this solution on YOUR website!
2x^2+4x+6
2(x^2+2x+3)

x=(-2+-sqrt[2^2-4*1*3])/2*1
x=(-2+-sqrt[4-12])/2
x=(-2+-sqrt-8)/2
x=(-2+-2.8284i)/2
x=-2/2+-2.8284i/2
x=-1+-1.4142i ans.

Question 236055: The Everton college store paid $1903 for an order of 49 calculators.The store paid $11 for each scientific calculaor. The others,all graphing calculators,cost the store $55 each. How many types of each calculator was ordered?
Found 2 solutions by jojo14344, stanbon:
Answer by jojo14344(1483)   (Show Source):
You can put this solution on YOUR website!

Let x= SC
and y=GC
Then,
, EQN 1

Also we know,
, EQN 2
we get, , EQN 3, subst. in EQN 1

---->
, number of GC, subst, in EQN 3

, number of SC

Check via EQN 1:

Thank you,
Jojo

Answer by stanbon(25959)   (Show Source):
You can put this solution on YOUR website!
The Everton college store paid $1903 for an order of 49 calculators.The store paid $11 for each scientific calculaor. The others,all graphing calculators,cost the store $55 each. How many types of each calculator was ordered?
----------------
Quantity Equation: c + g = 49
Value Equation::: 11c+55g = 1903
--------------------------------------
Multiply thru the Quantity Equation by 11 to get:
11c + 11g = 11*49
---
Subtract that Eq. from the Value Eq and solve for "g":
44g = 1903-11*49
g = 31 (# of graphing calculators bought)
------------------
Since c+g = 49, c = 18 (# of sci. calculators bought)
============================================================
Cheers,
Stan H.

Question 235987: How would you write the translation of 16 increased by b
Answer by rfer(2588)   (Show Source):
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16+b

Question 235961: I need to find the solution for h. the problem is 2h^2 - h - 3 = 0
Answer by stanbon(25959)   (Show Source):
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I need to find the solution for h. the problem is
2h^2 - h - 3 = 0
--------------
2h^2 - 3h + 2h -3 = 0
h(2h-3) + (2h-3) = 0
Factor:
(2h-3)(h+1) = 0
h = 3/2 or h = -1
========================
Cheers,
Stan H.

Question 235834: I am having a tough time with these problems on this one I must use the discriminate to determine the number of solutions of the quadratic equation and whether the solutions are real or complex. It is not necessary to find the roots just determine the number of types of solutions.
4/3x^2 - 2x + 3/4 =0
Answer by rfer(2588)   (Show Source):
You can put this solution on YOUR website!
the discriminant
b^2-4ac
------------------
4/3x^2-2x+3/4=0
a=4/3, b=-2, c=3/4
------------------
-2^2-4(4/3)(3/4)
----------------
Does that help?
Bob

Question 235891: For a quadratic function, how do you find the x-intercept(s)
Answer by nyc_function(155)   (Show Source):
You can put this solution on YOUR website!
To find the y-intercept, set x = 0 and solve for y.
To find the x-intercept, set y = 0 and solve for x.
Sample:
Given the function f(x) = -2x^2 - 5x + 4, find the intercepts.
Let x = 0 and solve for y.
f(0) = -2(0)^2 - 5(0) + 4
f(0) = 0 + 0 + 4
f(0) = 4
The y-intercept is the point (0,4).
==================================
Now, let y = 0 and solve for x.
Keep in mind that y = f(x). So, set f(x) = 0 and solve for x.
0 = -2x^2 - 5x + 4
2x^2 + 5x - 4 = 0
This quadratic only factors using the quadratic formula.
After doing the math, I got:
x = (-5 ± √57)/4
So, the x-intercepts are the points ((-5 +√57)/4), 0) and ((-5 -√57)/4), 0).
The reason I got this odd-looking x value is because the function I selected did not factor other than using the quadratic formula.

Question 235873:
27 + ( 3 x 6 ) / 2
I have no idea what the forward slash is standing for is it division?
Answer by Alan3354(5863)   (Show Source):
You can put this solution on YOUR website!
27 + ( 3 x 6 ) / 2
I have no idea what the forward slash is standing for is it division?
----
It is division
27 + ( 3 x 6 ) / 2
= 27 + 18/2
= 27 + 9
= 36
------
PS use * for multiplication, not x. x is often a variable term

Question 235833: I am having a tough time with these problems on this one I must use the discriminate to determine the number of solutions of the quadratic equation and whether the solutions are real or complex. It is not necessary to find the roots just determine the number of types of solutions.
2x^2+x-1=0
Answer by checkley77(6671)   (Show Source):
You can put this solution on YOUR website!
2x^2+x-1=0
(2X-1)(X+1)=0
2X-1=0
2X=1
X=1/2 ANS.
X+1=0
X=-1 ANS.

Question 235837: I have a tough time with word problems.
A rectangular parking lot is 50ft longer than it is wide. Determine the dimensions of the parking lot if it measures 250 ft diagonally
Answer by checkley77(6671)   (Show Source):
You can put this solution on YOUR website!
L=W+50
L^2+W^2=250^2
(W+50)^2+W^2=62,500
W^2+100W+2,500+W^2=62,500
2W^2+100W+2,500-62,500=0
2W^2+100W-60,000=0
2(W^2+50W-30,000)=0
2(W+200)(W-150)=0
W-150=0
W=150 ANS. FOR THE WIDTH.
L=150+50=200 ANS. FOR THE LENGTH.
PROOF:
200^2+150^2=250^2
40,000+22,500=62,500
62,500=62,500

Question 235838: I am having trouble with the story problems

Three consectutive even integers are such that the square of the third is 76 more than the square of the second, Find the three integers.
Answer by checkley77(6671)   (Show Source):
You can put this solution on YOUR website!
Let x, x+2 & x+4 be the 3 even integers.
(x+4)^2=(x+2)^2+76
x^2+8x+16=x^2+4x+4+76
x^2-x^2+8x-4x=-16+4+76
4x+64
x=64/4
x=16 ans. for the smallest integer.
16+2=18 ans. for the middle integer.
16+4=20 ans. for the largest integer.
Proof:
20^2=18^2+76
400=324+76
400=400

Question 235839: Another story problem I am having trouble with
A photo is 3 inches longer than it is wide. a 2-inch border is placed around the photo making the total area of the photo and border 108in^2. What are the dimensions of the photo
Answer by ankor@dixie-net.com(6567)   (Show Source):
You can put this solution on YOUR website!
A photo is 3 inches longer than it is wide. a 2-inch border is placed around the photo making the total area of the photo and border 108in^2.
What are the dimensions of the photo
:
Let x = the width of the photo
It says it is 3" longer than it is wide, therefore
(x+3) = the length of the photo
:
a two inch border will add 4 inches to the photo dimensions, therefore
(x+4) = width including the border
and
(x+3) + 4
which is
(x+7) = length including the border
:
Given that the area of the whole thing as 108 sq/in, therefore
(x+4) * (x+7) = 192
FOIL
x^2 + 7x + 4x + 28 = 192
:
x^2 + 11x + 28 - 192 = 0
:
x^2 + 11x - 164 = 0; our old friend, the quadratic equation!
:
Use the quadratic formula:

in this problem: a=1; b=11; c=-164

:

:

:

Positive solution

x =
x = 8.437" is the width of the photo
then
8.437 + 3 = 11.437" is the length
;
:
Check solution by finding the overall area
(8.437+4) * (11.437+4)) = 191.99 ~ 192

Question 235836: I am having a tough time with these problems on this one I must use the discriminate to determine the number of solutions of the quadratic equation and whether the solutions are real or complex. It is not necessary to find the roots just determine the number of types of solutions.
m^2 + m + 1 = 0
Answer by Theo(548)   (Show Source):
You can put this solution on YOUR website!

If you look at the graph, this equation should not have a solution.

The discriminant is equal b^2 - 4ac

The general form of a quadratic equation is:

ax^2 + bx + c

Your equation is:

m^2 + m + 1

Replace your "m" with "x" to get:

x^2 + x + 1

That makes your:

a = 1
b = 1
c = 1

a is the coefficient of the x^2 term.
b is the coefficient of the x term.
c is the constant term.

b^2 - 4ac becomes:

1^2 - 4*1*1 which becomes -3

A negative discriminant means your quadratic equation has no roots.

The quadratic formula used to solve quadratic equations is:

-b +/- sqrt(b^2-4ac) / 2a

Your discriminant of b^2-4ac is under the square root sign.

square root of negative 3 gives you an imaginary number which is not real.

Since the roots of a quadratic equation are the "real" values of x when y = 0, this equation has no roots.

The graph confirms that since the graph of the equation never crosses the x-axis.

Question 235506:
2x+2+ x - 1 = 180
Answer by Jeff Gordon(22)   (Show Source):
You can put this solution on YOUR website!
2x+2+ x - 1 = 180

combine terms

3x+1=180

subtract 1

3x=179

x=59.6

Question 235507:
4+3x+2+ 2x+ 3+4 = 180
Answer by Jeff Gordon(22)   (Show Source):
You can put this solution on YOUR website!
4+3x+2+ 2x+ 3+4 = 180

combine terms

5x+13=180

subtract 13

5x=167

x=33.4

Question 235510:
m+2 + m + 1 = 180
Answer by Jeff Gordon(22)   (Show Source):
You can put this solution on YOUR website!
2m+3=180

subtract 3

2m=180

m=90

Question 235727: What does x equal in the quadratic equation
please and thank you.
Found 2 solutions by josmiceli, Jeff Gordon:
Answer by josmiceli(2979)   (Show Source):
You can put this solution on YOUR website!

Subtract from both sides

Add to both sides

Use quadratic formula

and

The solutions are
and

Answer by Jeff Gordon(22)   (Show Source):
You can put this solution on YOUR website!
11x+1=180

subtract 1
11x= 179

x=16.28

Question 235622: 6.
Solve the equation by factoring.
z2 + 3z + 2 = 0 (1 point)
* z = –2 or z = –1
* z = –2 or z = 1
* z = 2 or z = –1
* z = 2 or z = 1
Answer by stanbon(25959)   (Show Source):
You can put this solution on YOUR website!
Solve the equation by factoring.
z^2 + 3z + 2 = 0
Factor:
(z+2)(z+1) = 0
z = -2 or z = -1
======================
Cheers,
Stan H.

Question 235626: 8.
Find the value of n such that x2 + 4x + n is a perfect square trinomial. (1 point)
* 8
* 2
* 4
* 16
Answer by Alan3354(5863)   (Show Source):
You can put this solution on YOUR website!
4
c = (b/2a)^2

Question 235508: For these problems I need use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions.
2x^2 + 5x + 5 = 0
Answer by stanbon(25959)   (Show Source):
You can put this solution on YOUR website!
just determine the number and types of solutions.
2x^2 + 5x + 5 = 0
---
a = 2 ; b = 5 ; c = 5
---
discriminant = b^2-4ac = 25 -4*2*5 = -15
=================================================
Since the discriminant is negative the
quadratic has two unequal Complex Number solutions.
=================================================
Cheers,
Stan H

Question 235498: What is the accumulated sum of each of the following streams of
payments?
a. $500 a year for 10 years compounded annually at 5 percent

Answer by stanbon(25959)   (Show Source):
You can put this solution on YOUR website!
What is the accumulated sum of each of the following streams of
payments?
a. $500 a year for 10 years compounded annually at 5 percent
-----------
A(t) = P(1+(r/n))^(nt)
----------------------------
A(10) = 500(1+(0.05/1)^(1*10)
A(10) = 500(1.05)^10
A(10) = 500*1.6289
A(10) = $814.45
====================
Cheers,
Stan H.

Question 235484: s(t)= -16t^2+200t+4

the quadratic function models the fireworks height, s(t) in feet, t seconds after they launch.
A. when should the fireworks go off so they explde at the greatest height?
B. what is the greatest height attainded by the fireworks?
Answer by solver91311(4818)   (Show Source):
You can put this solution on YOUR website!

If you graph the function you will see that it is a parabola opening downward -- which is to be expected because it is a quadratic function with a negative lead coefficient.

The maximum height will be reached at the coordinate of the vertex of the parabola. For the general quadratic function, , the -coordinate of the vertex is found by:

.

For your problem:

You can do your own arithmetic.

The maximum height is the value of the function at time , that is:

Again, the arithmetic is yours to perform.

John

Question 235457: -0.5x^+175x-3300=0
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(5863)   (Show Source):
You can put this solution on YOUR website!
-0.5x^+175x-3300=0
x^2 - 350x + 6600 = 0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=96100 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 330, 20. Here's your graph:

Answer by stanbon(25959)   (Show Source):
You can put this solution on YOUR website!
-0.5x^2+175x-3300=0
===
I graphed it and found a root at x = 20
-0.5(x^2-175x+3300) = 0
-0.5(x-20)(x-330)= 0
---
x = 20 or x = 330
=========================
Cheers,
Stan H.

Question 235423: what is the solution and working out to
Answer by checkley77(6671)   (Show Source):
You can put this solution on YOUR website!
4x^2-9x+11x-12=0
4x^2+2x-12=0
2(2x+x-6)=0
2(2x-3)(x+2)=0
2x-3=0
2x=3
x=3/2=1.5 ans.
x+2=0
x=-2 ans.

Question 235221: I am supposed to write a quadratic equation in the variable x as having the given numbers as a solution.Type the equation in standard form ax^2 + bx + c =0
Solution: 6 is the only solution
Answer by ankor@dixie-net.com(6567)   (Show Source):
You can put this solution on YOUR website!
I am supposed to write a quadratic equation in the variable x as having the given numbers as a solution.
Type the equation in standard form ax^2 + bx + c = 0
Solution: 6 is the only solution
:
FOIL: (x-6)(x-6) = x^2 - 6x - 6x + 36 = x^2 - 12x + 36 = 0

Question 235130: Solving Quadratic Equations by graphing; there is either 1, 2, or no real solutions... can you help me with this?
x^2-2x-24=0
Answer by solver91311(4818)   (Show Source):
You can put this solution on YOUR website!

First you want to graph the function

Then you want to find the one place that the graph of the function is tangent to the -axis, meaning that you have 1 real solution (actually, you would say that the equation has one real root with a multiplicity of two), or you want to find the two places that the graph intersects the -axis, meaning that you have two distinct real solutions, or you want to discover that the graph never touches the -axis, meaning that the equation has no real solutions.

What you are doing is answering the question, "What number or numbers can I substitute for so that ?" The function has a value of zero at the -axis.

Compare this to:

Notice two things: 1. The function is a perfect square trinomial. 2. The graph is tangent to the axis. One root with a multiplicity of 2.

No compare to:

Notice that the graph does not touch the -axis at all. No real solutions.

John

Question 235135: I need help with how to solve this:write a quadratic equation in standard form that passes through these points: (-1, 5), (0,3), (3,9).
I know it's a systems of equations, but the variables are confusing me... I got
5 = -A^2 - B + C
3 = C, and
9 = 3A^2 + 3B + C
I tried substituting 3 for c, but I don't know what to do from there
show work please and explain

Answer by jim_thompson5910(13679)   (Show Source):
You can put this solution on YOUR website!
Recall that each point is of the form (x,y). So for instance, the point (-1, 5) means x=-1 and y=5. This applies for each point given.

Also, remember that every quadratic can be represented as the equation:

where 'a', 'b' and 'c' are real numbers. These values are usually known (and we solve for 'x'), but in this case, we must set up a system of equations to find these values. Note: it turns out that there is only one unique solution to this problem.

So....

For the point (-1,5) we know that x=-1 and y=5. Since this point lies on the quadratic, we know that if we plug in x=-1 into the unknown quadratic, we know that we'll get y=5. So the idea is to plug in the given values to find the unknown values.

Plug these values into the general equation to get

Now square -1 to get 1, which means it will absorb into 'a', and simplify:

So the first equation we get is

--------------------------------------------

Furthermore, since the parabola goes through (0,3) we can plug in x=0 and y=3 to get which simplifies to . Because we've already isolated 'c', we can use this and plug it into the first equation to get . Now solve for 'a' to get . So whatever 'b' is, the value of 'a' will be 2 more than that.

--------------------------------------------

Finally, we see that the point (3,9) lies on the parabola. So just plug in x=3 and y=9 to get and simplify:

From here, we'll use the previously solved for variables 'a' and 'c' to find 'b':

Start with the given equation.

Plug in and

Distribute

Combine like terms.

Subtract 21 from both sides.

Combine like terms.

Divide both sides by 12 to isolate 'b'.

Reduce

So the value of 'b' is . Remember that we found that . So which means

So after everything is said and done, we find that , and giving us the quadratic

Notice how the parabola goes through the points (-1, 5), (0,3), and (3,9). So this visually confirms our answer.

Graph of through the points (-1, 5), (0,3), and (3,9)

Question 235119: I must use the quadratic formula to solve each equation. The one I'm having trouble with is in a different form to begin with and I can't figure out how to get it into standard form:
x= [2(x+3)]/(x+5)
I've tried distributing the numerator and then subtracting it from that side to the other side, and multiplying whats left of the fraction by its denominator, but its not working... PLEASE help! THANK YOU SO MUCH!
Answer by Edwin McCravy(2878)   (Show Source):
You can put this solution on YOUR website!

Clear of fractions by multiplying both sides by Get on the right: with , , and Edwin

Question 234850: I am just not understanding these type of problems. For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions.
z^2+z+1=0
Answer by ankor@dixie-net.com(6567)   (Show Source):
You can put this solution on YOUR website!
For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions.
:
You have to know the rules of the discriminate
we are talking about the quadratic form y = ax^2 = bx + c
:
The discriminate formula
d = b^2 - 4 * a * c
If d is positive: two real roots
If d = 0: two equal and real roots
If d = less than 0, (neg) no real roots, (complex)
:
z^2 + z + 1
:
In this problem
a = 1
b = 1
c = 1
:
The discriminate
d =
d = 1 - 4
d = -3, negative, no real roots, complex

Question 234851: For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions
(3)^1/2y^2 -4y-7(3)^1/2=0
Answer by ankor@dixie-net.com(6567)   (Show Source):
You can put this solution on YOUR website!
For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions
:
You have to know the rules of the discriminate
we are talking about the quadratic form y = ax^2 = bx + c
:
The discriminate formula
d = b^2 - 4 * a * c
If d is positive: two real roots
If d = 0: two equal and real roots
If d = less than 0, (neg) no real roots, (complex)
:
(3)^1/2y^2 -4y-7(3)^1/2=0
:
^1/2 = square root so we can write the equation:
= 0
:
In this problem
a =
b = -4
c =
:
The discriminate
d =
we have a square root times a square root so we have
d = 16 - 4 * 3 * (-7)
d = 16 - (-84)
d = 16 + 84
d = 100, well positive, two real roots on this quad equation

Question 235022: Employees of a discount appliance store receive an additional 20% off of the lowest price on an item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450?
Answer by josmiceli(2979)   (Show Source):
You can put this solution on YOUR website!

and

He will pay $306

Question 235008: how do you solve and check this algebra equation 2/3x=42
Answer by Stitch(34)   (Show Source):
You can put this solution on YOUR website!
Given:
Multiply both sides by 3/2

The 3/2 & the 2/3 cancel out on the left side of the equation
rewrite the equation
Simplify

To check your work, plug 63 into the given equation for X

42 = 42

Question 234995: X sqaured-6x=135
Answer by Stitch(34)   (Show Source):
You can put this solution on YOUR website!
Given:
Rewrite the equation as
This equation can be foiled.
First find the factors of 135.
They are: 1,3,5,9,15,27,45,135
9 and 15 fit for this equation.
These two equations are equal
Now
We have 2 solutions
X + 9 = 0 or rewritten as X = -9
& X - 15 = 0 or rewritten as X = 15