Question

graph the parabola.
$y = \frac{1}{4}x^2$
plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. then click on the graph - a - function button.

Explanation:

Step1: Find the vertex

For $y=\frac{1}{4}x^2$, vertex is at $x=0$. Substitute $x=0$:
$y=\frac{1}{4}(0)^2=0$
Vertex: $(0,0)$

Step2: Pick left x-values, solve for y

Choose $x=-2, -4$:
For $x=-2$: $y=\frac{1}{4}(-2)^2=\frac{1}{4}(4)=1$ → $(-2,1)$
For $x=-4$: $y=\frac{1}{4}(-4)^2=\frac{1}{4}(16)=4$ → $(-4,4)$

Step3: Pick right x-values, solve for y

Choose $x=2, 4$:
For $x=2$: $y=\frac{1}{4}(2)^2=\frac{1}{4}(4)=1$ → $(2,1)$
For $x=4$: $y=\frac{1}{4}(4)^2=\frac{1}{4}(16)=4$ → $(4,4)$

Answer:

Plot the five points:

1. Vertex: $(0, 0)$
2. Left points: $(-2, 1)$, $(-4, 4)$
3. Right points: $(2, 1)$, $(4, 4)$

Then connect the points to graph the parabola $y=\frac{1}{4}x^2$.