Question

Complete the statements below that show y = 8x2 + 32x + 17 being converted to vertex form. Factor out the leading coefficient. y = 8(x2 + 4x) + 17 Form a perfect-square trinomial. y = 8(x2 + 4x + ) + 17 +

Answer 1

8(x^2 + 4x +4) + 17 + -32

Answer 2

ANSWER

$y=8(x^2+4x+4)+17-32$

EXPLANATION

We were given $y=8x^2+32x+17$.

To convert to vertex form, We factor out the leading coefficient which is 8.

$y=8(x^2+4x)+17$

Next, we form a perfect square by adding and subtracting $8(2)^2$ to get;

$y=8(x^2+4x)+8(4)+17-8(4)$

We factor and combine the first two terms with a common factor of 8 to get,

$y=8(x^2+4x+4)+17-8(4)^2$

This simplifies to

$y=8(x^2+4x+4)+17-32$