Question

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

For $f(x)=-x^2$, which is in the form $f(x)=ax^2+bx+c$ with $a=-1$, $b=0$, $c=0$. The vertex of $ax^2+bx+c$ is at $x=-\frac{b}{2a}$.
$x=-\frac{0}{2(-1)}=0$. Substitute $x=0$: $f(0)=-(0)^2=0$. Vertex is $(0,0)$.

Step2: Find a second point

Choose $x=2$. Substitute into $f(x)$:
$f(2)=-(2)^2=-4$. The point is $(2,-4)$.

Step3: Use symmetry for third point

Parabolas are symmetric about the vertex (the y-axis here). The mirror of $(2,-4)$ across the y-axis is $(-2,-4)$.

Answer:

1. Plot the vertex at $(0, 0)$.
2. Plot the point $(2, -4)$ and its symmetric point $(-2, -4)$.
3. Draw a downward-opening parabola passing through these points.