SOLUTION: convert to vertex form y=-3x^2-24x-46

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Question 960120: convert to vertex form
y=-3x^2-24x-46
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you have to group the x^2 and x together to get:

y = (3x^2 - 24x) - 46

you have to factor out the 3 so that the x^2 term has a coefficient of 1.

y = 3 * (x^2 - 8x) - 46

you have to complete the squares on (x^2 - 8x)

divide the coefficient of the x term by 2 and you will get 4.

square the 4 and you will get 16.

(x^2 - 8x) will become equal to (x-4)^2 - 16

3 * (x^2 - 8x) - 46 will become equal to:

3 * ((x-4)^2 - 16) - 46 which will become equal to:

3 * (x-4)^2 - 48 - 46 which will become equal to:

3 * (x-4)^2 - 94.

that's the vertex form of the equation.

you started with:

y = 3x^2 - 24x - 46

you ended up with:

y = 3 * (x-4)^2 - 94

those two equations are equivalent.

if you graph both equations, they will generate the same graph.

that graph is shown below:

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