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=-(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=(1)/(3)x^2`

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

Using the formula:

`x_v=-(0)/(2\cdot1)=0`

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

`y=(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} (1)/(3)\cdot(-6)^2=(36)/(3)=12 \\ (1)/(3)\cdot(-3)^2=(9)/(3)=3 \\ (1)/(3)\cdot3^2=(9)/(3)=3 \\ (1)/(3)\cdot6^2=(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)