Question

I need help with graphing 5 points. 2 points to the left of vertex, the vertex, 2 points to the right of the vertex. graph goes up to 14

Answer 1

Quadratic function in vertex form:

$y=a(x-h)^2+k$

(h,k) is the vertex.

For the given quadratic function (parabola):

$y=(x-5)^2-1$

The vertex is the point: (5,-1)

To find the two point on the left of the vertex, use the equation and find its value when x is two values that are less than 5:

When x=4

$\begin{gathered} y=(4-5)^2-1 \\ y=(-1)^2-1 \\ y=1-1 \\ y=0 \end{gathered}$

Point (4,0)

When x=3

$\begin{gathered} y=(3-5)^2-1 \\ y=(-2)^2-1 \\ y=4-1 \\ y=3 \end{gathered}$

Point (3,3)

To find the two point on the right of the vertex, use the equation and find its value when x is two values that are greater than 5:

When x=6

$\begin{gathered} y=(6-5)^2-1 \\ y=1^2-1 \\ y=1-1 \\ y=0 \end{gathered}$

Point (6,0)

When x=7

$\begin{gathered} y=(7-5)^2-1 \\ y=2^2-1 \\ y=4-1 \\ y=3 \end{gathered}$

Point (7,3)

Then, you have the next points to graph the parabola:

Vertex: (5,-1)

To the left of the vertex: (4,0) and (3,3)

To the right of the vertex: (6,0) and (7,3)

Graph: