SOLUTION: 1. Rewrite y = x2 + 14x + 29 in general form. 2. Rewrite y = 3x2 - 24x + 10 in general form. 3. Solve for x: (x - 9)2 = 1 4. Solve for x: x2 + 24x + 90 = 0 5. Solve for x:

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Question 462262: 1. Rewrite y = x2 + 14x + 29 in general form.
2. Rewrite y = 3x2 - 24x + 10 in general form.
3. Solve for x: (x - 9)2 = 1
4. Solve for x: x2 + 24x + 90 = 0
5. Solve for x: 2x2 - 4x - 14 = 0
6. Create your own quadratic equation and demonstrate how it would be solved by graphing, factoring, the quadratic formula, and by completing the square.

Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
first: Quadratic Functions in General Form is or


1....already in general form.

2. ...already in general form.
3. Solve for :








4. Solve for :
....use quadratic formula
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic





the general solution using the quadratic equation is:







So lets solve ( notice , , and )





Plug in a=1, b=24, and c=90




Square 24 to get 576




Multiply to get




Combine like terms in the radicand (everything under the square root)




Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


or



Now break up the fraction



or



Simplify



or



So the solutions are:

or





5. Solve for :
....use quadratic formula
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic





the general solution using the quadratic equation is:







So lets solve ( notice , , and )





Plug in a=2, b=-4, and c=-14




Negate -4 to get 4




Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because .)




Multiply to get




Combine like terms in the radicand (everything under the square root)




Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




Multiply 2 and 2 to get 4


So now the expression breaks down into two parts


or



Now break up the fraction



or



Simplify



or



So the solutions are:

or




6. Create your own quadratic equation and demonstrate how it would be solved by graphing, factoring, the quadratic formula, and by completing the square.

....use quadratic formula
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic





the general solution using the quadratic equation is:







So lets solve ( notice , , and )





Plug in a=1, b=3, and c=2




Square 3 to get 9




Multiply to get




Combine like terms in the radicand (everything under the square root)




Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


or


Lets look at the first part:





Add the terms in the numerator

Divide


So one answer is






Now lets look at the second part:





Subtract the terms in the numerator

Divide


So another answer is




So our solutions are:

or




....use graphing
find first several points that lie on a parabola
if ...->...

if ...->...
if ...->...
if ...->...
if ...->...


....use factoring
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor , first we need to ask ourselves: What two numbers multiply to 2 and add to 3? Lets find out by listing all of the possible factors of 2


Factors:

1,2,

-1,-2,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 2.

1*2=2

(-1)*(-2)=2

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 3

||
First Number|Second Number|Sum
1|2|1+2=3
-1|-2|-1+(-2)=-3
We can see from the table that 1 and 2 add to 3. So the two numbers that multiply to 2 and add to 3 are: 1 and 2 Now we substitute these numbers into a and b of the general equation of a product of linear factors which is: substitute a=1 and b=2 So the equation becomes: (x+1)(x+2) Notice that if we foil (x+1)(x+2) we get the quadratic again


....use completing the square
convert it into



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