Question

graph the function $f(x) = -4x^2$. 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: Find the vertex

For $f(x)=ax^2+bx+c$, vertex at $x=-\frac{b}{2a}$. Here $a=-4, b=0$, so $x=0$. Substitute $x=0$: $f(0)=-4(0)^2=0$. Vertex is $(0,0)$.

Step2: Find another point

Choose $x=1$. Substitute into $f(x)$: $f(1)=-4(1)^2=-4$. Point is $(1,-4)$.
(Note: Due to symmetry, $(-1,-4)$ is also a valid point.)

Answer:

1. Plot the vertex at $(0, 0)$.
2. Plot a second point at $(1, -4)$ (or $(-1, -4)$), then draw a downward-opening parabola passing through these points.