Question

graph the function $f(x) = -3x^2$. 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 $a=-3, b=0$, so $x=0$. Substitute $x=0$: $f(0)=-3(0)^2=0$. Vertex is $(0,0)$.

Step2: Find a second point

Choose $x=1$. Substitute into $f(x)$: $f(1)=-3(1)^2=-3$. Point is $(1,-3)$.

Step3: Use symmetry for third point

Parabola is symmetric over $x=0$, so $x=-1$ gives $f(-1)=-3(-1)^2=-3$. Point is $(-1,-3)$.

Answer:

1. Plot the vertex at $(0, 0)$.
2. Plot the point $(1, -3)$ (and $(-1, -3)$ for symmetry), then draw a downward-opening parabola passing through these points.