Question

graph the function $f(x) = -5(x - 4)^2$. plot the vertex. then plot another point on the parabola. if you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

Explanation:

Step1: Identify vertex form

The function is in vertex form $f(x)=a(x-h)^2+k$, where $(h,k)$ is the vertex.
For $f(x)=-5(x-4)^2$, $h=4$, $k=0$.

Step2: Find vertex coordinates

Vertex is $(h,k)=(4, 0)$.

Step3: Choose x-value, compute f(x)

Pick $x=3$, substitute into the function:
$f(3)=-5(3-4)^2=-5(-1)^2=-5(1)=-5$
This gives the point $(3, -5)$.

Step4: Choose another x-value, compute f(x)

Pick $x=5$, substitute into the function:
$f(5)=-5(5-4)^2=-5(1)^2=-5(1)=-5$
This gives the point $(5, -5)$.

Answer:

1. Plot the vertex at $(4, 0)$.
2. Plot additional points such as $(3, -5)$ and $(5, -5)$, then draw a downward-opening parabola through these points.