Question

graph the function.
$f(x)=-\frac{1}{2}(x - 2)^2-4$

Explanation:

Step1: Identify vertex

Vertex \((h,k)=(2,-4)\)

Step2: Determine direction

\(a=-\frac{1}{2}<0\), opens downward

Step3: Find x=0 point

\(f(0)=-\frac{1}{2}(0-2)^2-4=-6\), point \((0,-6)\)

Step4: Find x=4 point

\(f(4)=-\frac{1}{2}(4-2)^2-4=-6\), point \((4,-6)\)

Step5: Plot & draw

Plot vertex \((2,-4)\), \((0,-6)\), \((4,-6)\); draw downward parabola

Answer:

The graph is a downward-opening parabola with vertex at (2, -4), passing through (0, -6) and (4, -6).