Complete the square to write the equation "y=3x^2+6x-24" in graphing form?

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Complete the square to write the equation "y=3x^2+6x-24" in graphing form?

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Answer 1 · 2018-05-20T01:32:29

$y = 3 {(x + 1)}^{2} - 27$ $y =3(x +1)^2 -27$

vertex is $(- 1, - 27)$ $(-1, -27)$

Explanation:

vetex form is:

$y = a {(x - h)}^{2} + k$ $y = a(x-h)^2+k$ and the vertex is $(h, k)$ $(h, k)$

to get vertex form we must complete the square:

$y = 3 x^{2} + 6 x - 24$ $y=3x^2+6x-24$

isolate the x terms:

$y + 24 = 3 x^{2} + 6 x$ $y +24 =3x^2+6x$

factor out 3 so the coefficient of $x^{2}$ $x^2$ is 1 which is required to complete the square:

$y + 24 = 3 (x^{2} + 2 x)$ $y +24 =3(x^2+2x)$

now complete the square

$a x^{2} + b x + c$ $ax^2 +bx +c$ , a = 1, $c = {(\frac{1}{2} b)}^{2}$ $c= (1/2b)^2$

$c = {(\frac{1}{2} (2))}^{2} = 1^{2} = 1$ $c=(1/2(2))^2 = 1^2 = 1$

$y + 24 + 3 c = 3 (x^{2} + 2 x + c)$ $y +24 +3c=3(x^2+2x +c)$ notice $3 c$ $3c$ added to the left side, that is because we have to add the same value to both sides and the right side has 3 factored out.

replace the $c$ $c$

$y + 24 + 3 (1) = 3 (x^{2} + 2 x + 1)$ $y +24 +3(1)=3(x^2+2x +1)$

finish the square:

$y + 27 = 3 {(x + 1)}^{2}$ $y +27=3(x +1)^2$

$y = 3 {(x + 1)}^{2} - 27$ $y =3(x +1)^2 -27$

so our vertex is $(- 1, - 27)$ $(-1, -27)$

remember the form is $y = a {(x - h)}^{2} + k$ $y = a(x-h)^2+k$ so the sign of the h term changes.

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Complete the square to write the equation "y=3x^2+6x-24" in graphing form?

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