Question

graph ( h(x) = 0.5(x + 2)^2 - 4 ) by following these steps:
step 1: identify ( a ), ( h ), and ( k ).
( a = 0.5 ) ( h = -2 ) ( k = -4 )
step 2: plot the vertex at ( (-2, -4) ).
step 3: the axis of symmetry is the line ( x = -2 ).
step 4: evaluate the function at two other ( x )-values:
( h(-4) = ) ( h(-6) = )
(there are also some interface elements like a dropdown with -2, 2, 4 and a check button, and a graph with coordinate axes and a table at the bottom which is partially visible)

Explanation:

Step1: Calculate $h(-4)$

Substitute $x=-4$ into $h(x)$:
$$h(-4)=0.5(-4+2)^2 - 4 = 0.5(-2)^2 - 4 = 0.5\times4 - 4 = 2 - 4 = -2$$

Step2: Calculate $h(-6)$

Substitute $x=-6$ into $h(x)$:
$$h(-6)=0.5(-6+2)^2 - 4 = 0.5(-4)^2 - 4 = 0.5\times16 - 4 = 8 - 4 = 4$$

Answer:

$h(-4) = -2$, $h(-6) = 4$

To complete the graph, plot the points $(-4, -2)$ and $(-6, 4)$, then reflect them across the axis of symmetry $x=-2$ to get $(-0, -2)$ and $(2, 4)$, then draw a smooth parabola through all points including the vertex $(-2, -4)$.