Question

graph the parabola.
y = 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 the parabola $y = x^{2}$, the vertex - form of a parabola is $y=a(x - h)^{2}+k$, where $(h,k)$ is the vertex. In $y = x^{2}$, $a = 1$, $h = 0$, and $k = 0$. So the vertex is $(0,0)$.

Step2: Find points to the left of the vertex

Let $x=-1$, then $y=(-1)^{2}=1$. Let $x = - 2$, then $y=(-2)^{2}=4$. The two points to the left of the vertex are $(-1,1)$ and $(-2,4)$.

Step3: Find points to the right of the vertex

Let $x = 1$, then $y=(1)^{2}=1$. Let $x = 2$, then $y=(2)^{2}=4$. The two points to the right of the vertex are $(1,1)$ and $(2,4)$.

Answer:

The five points are $(0,0),(-1,1),(-2,4),(1,1),(2,4)$