Question

graphing a quadratic function in vertex form
graph ( h(x) = 0.5(x + 2)^2 - 4 ) by following these steps:

step 1: identify ( a ), ( h ), and ( k ).
( a = ) dropdown with options 0.5, 2, 4
(graph and table omitted as per ocr instructions)

Explanation:

Step1: Recall vertex form

The vertex form of a quadratic function is $h(x) = a(x - h)^2 + k$.

Step2: Match given function to form

The given function is $h(x) = 0.5(x + 2)^2 - 4$, which can be rewritten as $h(x) = 0.5(x - (-2))^2 + (-4)$. Compare to the vertex form to identify $a$.

Answer:

$a = 0.5$