Question

5 fill in the blank 25 points consider the quadratic function: ( h(x) = x^2 - 10x + 12 ). fill in the blanks to rewrite the function into vertex form, ( y = (x - h)^2 + k ), by completing the square. ( y = (x - \text{type your answer...})^2 + \text{type your answer...} )

Explanation:

Step1: Group 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 filled with 5 and -13 respectively.