Question

graph the parabola.
$y = \frac{1}{2}x^2$
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 - function button.

Explanation:

Step1: Find the vertex

For $y=\frac{1}{2}x^2$, the vertex form is $y=a(x-h)^2+k$ with $h=0,k=0$. Vertex: $(0,0)$

Step2: Pick left x-values, solve for y

Choose $x=-2, x=-1$:
$x=-2$: $y=\frac{1}{2}(-2)^2=\frac{1}{2}(4)=2$ → $(-2,2)$
$x=-1$: $y=\frac{1}{2}(-1)^2=\frac{1}{2}(1)=0.5$ → $(-1, 0.5)$

Step3: Pick right x-values, solve for y

Choose $x=1, x=2$:
$x=1$: $y=\frac{1}{2}(1)^2=0.5$ → $(1, 0.5)$
$x=2$: $y=\frac{1}{2}(2)^2=2$ → $(2,2)$

Answer:

Five points to plot:

1. Vertex: $(0, 0)$
2. Left of vertex: $(-2, 2)$, $(-1, 0.5)$
3. Right of vertex: $(1, 0.5)$, $(2, 2)$

Connect these points to graph the parabola $y=\frac{1}{2}x^2$.