Question

consider the quadratic function: h(x) = x² - 10x + 12. fill in the blanks to rewrite the function into vertex form, y = (x - h)² + k, by completing the square. y = (x - type your answer... )² + type your answer...

Explanation:

Step1: Isolate x terms

$h(x) = (x^2 - 10x) + 12$

Step2: Complete the square

Take half of -10: $\frac{-10}{2} = -5$, square it: $(-5)^2 = 25$. Add and subtract 25 inside the parentheses:
$h(x) = (x^2 - 10x + 25 - 25) + 12$

Step3: Rewrite as perfect square

$h(x) = (x - 5)^2 - 25 + 12$

Step4: Simplify constant terms

$h(x) = (x - 5)^2 - 13$

Answer:

$y=(x - 5)^2 + (-13)$
The blanks are 5 and -13 respectively.