Question

graph ( h(x) = 0.5(x + 2)^2 - 4 ) by following these steps:
step 1: identify ( a ), ( h ), and ( k ).
( a = )
options: 0.5, 2, 4

Explanation:

Step1: Match to vertex form

The vertex form of a quadratic function is $h(x) = a(x-h)^2 + k$. Rewrite the given function to match:
$h(x) = 0.5(x - (-2))^2 + (-4)$

Step2: Identify $a, h, k$

Extract values from the matched form:
$a = 0.5$, $h = -2$, $k = -4$

Step3: Find vertex point

The vertex is $(h, k)$:
$(h, k) = (-2, -4)$

Step4: Generate sample points

Choose $x$-values around $h$ and calculate $y$:

• For $x=0$: $h(0)=0.5(0+2)^2-4=0.5(4)-4=2-4=-2$
• For $x=-4$: $h(-4)=0.5(-4+2)^2-4=0.5(4)-4=2-4=-2$
• For $x=2$: $h(2)=0.5(2+2)^2-4=0.5(16)-4=8-4=4$
• For $x=-6$: $h(-6)=0.5(-6+2)^2-4=0.5(16)-4=8-4=4$

Answer:

• $a=0.5$, $h=-2$, $k=-4$
• Sample $(x,y)$ points:

$(-6, 4)$, $(-4, -2)$, $(-2, -4)$, $(0, -2)$, $(2, 4)$

• The graph is a upward-opening parabola with vertex at $(-2, -4)$ passing through the listed points.