Question

graph the parabola. need 5 points. 2 to the left if vertex, the vertex, and 2 to the right of the vertex

Answer 1

Given:

`y=x^2`

Let's graph the parabola.

To graph the parabola, apply the vertex form of a parabola:

`\begin{gathered} y=a(x-h)^2+k \\ \\ y=1(x-0)^2+0 \end{gathered}`

Thus, we have the values:

a = 1

h = 0

k = 0.

• The vertex is:

(h, k) ==> (0, 0)

• The parabola opens up since the value of ,a ,is positive.

Now, let's find more points using the equation.

• When x = 1

`\begin{gathered} y=1^2 \\ y=1 \end{gathered}`

When x = -1:

`\begin{gathered} y=-1^2 \\ y=1 \end{gathered}`

When x = 2:

`\begin{gathered} y=2^2 \\ y=4 \end{gathered}`

When x = -2:

`\begin{gathered} y=-2^2 \\ y=4 \end{gathered}`

When x = 3:

`\begin{gathered} y=3^2 \\ y=9 \end{gathered}`

When x = -3:

`\begin{gathered} y=-3^2 \\ y=9 \end{gathered}`

Therefore, we have the points:

(0, 0), (1, 1), (-1, 1), (2, 4), (-2, 4), (3, 9), (-3, 9)

Plot the points and connect them to form a parabola.

We have the graph below: