Question

graph the function $f(x) = 5x^2$. 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 of $f(x)=5x^2$

For $f(x)=ax^2+bx+c$, vertex is at $x=-\frac{b}{2a}$. Here $a=5, b=0$, so $x=0$. Substitute $x=0$: $f(0)=5(0)^2=0$. Vertex: $(0,0)$.

Step2: Find a second point on the parabola

Choose $x=1$. Substitute into $f(x)$: $f(1)=5(1)^2=5$. Point: $(1,5)$.

Step3: Use symmetry for a third point

Parabola is symmetric over $x=0$, so $x=-1$ gives $f(-1)=5(-1)^2=5$. Point: $(-1,5)$.

Answer:

1. Plot the vertex at $(0, 0)$.
2. Plot the point $(1, 5)$ (and $(-1, 5)$ for symmetry), then draw a upward-opening parabola passing through these points.