SOLUTION: 2) Solve for x. 5x^2=-19x-12 ___________ ___________ ___________ ___________ ___________ ___________ ___________ 3) f(x)=-(x+2)^2-7 The vertex is: _____ (type an ordered pair)

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Question 471134: 2) Solve for x.
5x^2=-19x-12
___________________________________________________________________________________
3) f(x)=-(x+2)^2-7
The vertex is: _____ (type an ordered pair)
The line of symmetry is x=_____
The maximum and minimum value of f(x) is______
The value, f(-2)=-7 is _____
a)Maximus
b)Minimum
_______________________________________________________________________________
4) Solve the formula for the given letter. Assume all variables represents nonnegative numbers.
a^2+q^2=g^2,for a
Choose the correct value for
1)a –√(g^2-q^2 )
2)√(g^2-q^2 )
3)g^2-q^2
______________________________________________________________________________
5)Determine the nature of the solutions of the equations.
y^2=4/7 y+1/2
Choose the correct answer below:
a) The equation has one real solution
b) The equation has two real solutions
c) The equation has two non-real solutions
______________________________________________________________________________
7) Find the vertex, the line of symmetry, and the maximum or minimum value of f(x).
f(x)=1/3(x+2)^2+3
The vertex is____(type an ordered pair)
The line of symmetry is x=_____
What is the maximum/minimum value of f(x)?_____
Is the value, f(-2)=3 a minimum or maximum?
a)Maximum
b)Minimum
________________________________________________________________________
8) Determine the nature of the solutions of the equation.
x^2-4x+4=0
What does the equations have?
a)Two real solutions
b)One real solution
c)Two non-real solutions
_______________________________________________
9) Give exact and approximate solutions to three decimal places
x^2-5x+3=0
The exact solutions are x=____
The approximate solutions to 3 decimal places are x=____
________________________________________________________________________________
10) Solve by completing the square.
x^2+5/2 x=5
What is the solution? X=_____
__________________________________________________
11) A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 80 ft of fence? What should the dimensions of the garden be to given this area.
The maximum area that the farmer can enclose with 80 ft of fence is ___ sq ft.
The dimensions of the garden to give this area is 40 ft by ___ ft
___________________________________________________________________________
12)Find and label the vertex and the line of symmetry.
f(x)=-3(x+2)^2
The vertex is _____(type an ordered pair)
The equation of the line symmetry is x=____
__________________________________________________________________
13) Find and label the vertex and the line of symmetry.
f(x)=1/4 x^2
The vertex is _____(type an ordered pair)
________________________________________________________________________
14) The width of a rectangle is 1 ft less the length. The area is 6 ft^2. Find the length and the width.
The width is ___ ft
The length is ____ft
__________________________________________________________
15)Find the vertex, the line of symmetry, the maximum or minimum value of the quadractic function
f(x)=x^2-8x-4
What is the vertex?___(type an ordered pair)
What is the equation of the line of symmetry?____
What is the maximum/ minimum of f(x)?_____
Is the value, f(4)=-2 a minimum or maximum?
_______________________________________________________________________
16)A student opens a mathematics book to two facing pages. The product of the page number is 930. Find the page numbers.
The first page is___
The second page is ____
___________________________________________________________________________
17) Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function.
f(x)=3x^2-6x+6
The vertex is___(type an order pair)
Choose the correct line of symmetry below.
a)Y=3
b)X=1
c)Y=-3
d)X=-1
The maximum/ minimum of f(x) is_______
Is the value, f(1)=3 a minimum or a maximum?_________
___________________________________________________________________
18) Solve 3x^2-7x-13=0
Find the x- intercepts of f(x)= 3x^2-7x-13
What are the solutions? X=______ (type exact answers, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed)
What are the x- intercepts?_____( Type ordered pairs. Type an exact answer, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed)
_______________________________________________________________________
19) What a quadratic equation in the variable x having the given numbers as solution. Type the equation in standard form,ax^2+bx+c=0
Solution:5, only solution.
The equation is ___=0
______________________________________________________________________
20)Find the vertex, line symmetry, the maximum or minimum value of the quadratic function.
f(x)-2x^2+2x+10
The x- coordinate of the vertex is___( type a simplified fraction)
The y-coordinate of the vertex is___(type a simplified fraction)
The equation of the line symmetry is x=____(Type a simplified fraction)
The maximum/ minimum of f(x) is ____(Type a simplified fraction)
The value, f(1/2)=21/2 is?
a)Maximum
b)Minimum
_____________________________________________________________
21) Find the x and y intercepts
f(x)=16x^2+8x+1
The y intercept is ___( Type an ordered pair)
The x intercept is ___(Type an ordered pair)
___________________________________________________________________
22)Give exact and approximate solutions to three decimal places.
x^2+16x+64=16
What are the exact solution? X=____ (type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.
___________________________________________________________
23) Give exact and approximate solution to three decimal places.
(x+3)^2=64
What are the exact solutions? X=____(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use comma to separate answers as needed)
There are no approximate solutions since the solution are intergers.

Found 2 solutions by Alan3354, ewatrrr:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
22)Give exact and approximate solutions to three decimal places.
x^2+16x+64=16
--------------

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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=64 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -4, -12. Here's your graph:

-----------------------
It's not likely anyone will do all those for you, unless you show your efforts.
Maybe not then, but your chances are better.
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi,

The site recommends posting no more than 1 Question per post.

Following all do relate to:

the vertex form of a parabola opening up or down,  

where(h,k) is the vertex. a> 0 Vertex a minimum point.  a<0 Vertex a maximum Pt

3)  f(x)=-(x+2)^2-7   V(-2,-7) -1<0 Maximum Pt x = -2 Line of symmetry

7)  f(x)=1/3(x+2)^2+3 V(-2,3) 1/3>0 Minimum Pt x = -2 Line of symmetry



12) f(x)=-3(x+2)^2 V(-2,0) -3<0 Maximum Pt x = -2 Line of symmetry



13) f(x)=1/4 x^2  V(0,0) 1/4>0 Minimum Pt Pt x = 0(y-axis) Line of symmetry

following involve completing the Square

15) f(x)=x^2-8x-4 

    f(x) = 1*(x-4)^2 -20 V(4,-20) 1>0 Minimum Pt x = 4 Line of symmetry



17) f(x)=3x^2-6x+6

    f(x) = 3(x-1)^2 +3 V(1,3) 3>0 Maximum Pt x = 1 Line of symmetry



20) f(x)=2x^2+2x+10

    f(x)= 2(x+1/2)^2 + 9.5 V(-1/2,9.5) 2>0 Minimum Pt x = -1/2 Line of symmetry





 

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