Question

write h(x) = 7 + 10x + x² in vertex form.

1. write h in standard form.

h(x) = x² + 10x + 7

1. form a perfect square trinomial by adding and subtracting (\frac{b}{2})².

h(x) = (x² + 10x + \underline{25}) + 7 - \underline{25}

1. write the trinomial as a binomial squared.
2. write the function in vertex form, if needed.

what is h(x) = 7 + 10x + x² written in vertex form?
options:

• h(x) = (x + 25)² + 32
• h(x) = (x - 25)² - 18
• h(x) = (x + 5)² - 18

Explanation:

Step1: Rearrange to standard form

$h(x) = x^2 + 10x + 7$

Step2: Add/subtract $(\frac{10}{2})^2=25$

$h(x) = (x^2 + 10x + 25) + 7 - 25$

Step3: Rewrite trinomial as binomial square

$h(x) = (x+5)^2 + 7 - 25$

Step4: Simplify constant terms

$h(x) = (x+5)^2 - 18$

Answer:

$h(x) = (x+5)^2 - 18$