complete the statements below that show y = 8x² + 32x + 17 being converted to vertex form. factor out the…

Explanation:

Step1: Recall perfect - square trinomial formula

For a quadratic expression of the form (ax^{2}+bx + c) to be a perfect - square trinomial, when (a = 1), (c=\left(\frac{b}{2}\right)^{2}). In the expression (x^{2}+4x), if we want to make it a perfect - square trinomial, since (b = 4), then (\left(\frac{b}{2}\right)^{2}=\left(\frac{4}{2}\right)^{2}=4).

Step2: Analyze the effect of factoring on the constant term

We factored out a (8) from the first two terms. When we add (4) inside the parentheses ((y = 8(x^{2}+4x + 4)+17+\square)), we are actually adding (8\times4) to the original expression. To keep the equation balanced, we need to subtract (8\times4) from the expression. So we subtract (32) from the constant term outside the parentheses.

Answer:

The first blank is (4) and the second blank is (- 32)