Question

need 5 points. the vertex, 2 points to the left of vertex, & 2 points to the right of vertex

Answer 1

The x-coordinate of the vertex of a parabolla is:

$x_v=-\frac{b}{2a}$

And b and a, correspond to the standard form of a parabolla:

$y=ax^2+bx+c$

In this case, we have the parabolla:

$y=\frac{1}{3}x^2$

Then, the a = 1/3 and b = 0

Using the formula:

$x_v=-\frac{0}{2\cdot1}=0$

Then to find the y coordinate of the vertex, we evaluate the function in x = 0:

$y=\frac{1}{3}\cdot0^2=0$

The coordinate of the vertex is (0, 0)

Now to find two points on the left and two on the right, we just need to evaluate the function of x at the left and in the right of 0:

Let's use -6, -3, 3, 6

$\begin{gathered} \frac{1}{3}\cdot(-6)^2=\frac{36}{3}=12 \\ \frac{1}{3}\cdot(-3)^2=\frac{9}{3}=3 \\ \frac{1}{3}\cdot3^2=\frac{9}{3}=3 \\ \frac{1}{3}\cdot6^2=\frac{36}{3}=12 \end{gathered}$

Then the vertex is at:

(0, 0)

We have two points at the left:

(-6, 12)

(-3, 3)

And two to the right:

(3, 12)

(6, 12)