Question

Graph the parabola.y = x ^ 2 - 6Plot 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.

Answer 1

Step 1

Find the vertex (h,k)

$\begin{gathered} h=-\frac{b}{2a} \\ k=f\mleft(h\mright) \end{gathered}$$\begin{gathered} a=1 \\ b=0 \\ h=-\frac{0}{2\times1}=0 \\ k=\left(0\right)-6=-6 \end{gathered}$

The vertex=(0,-6)

Step 2

Find two points to the left

$\begin{gathered} when\text{ y=0} \\ 0=x^2-6 \\ x=\pm\sqrt{6} \\ when\text{ x=-2} \\ y=\left(-2\right)^2-6 \\ y=4-6=-2 \\ The\text{ two points are \lparen-}\sqrt{6},0)\text{ and \lparen-2,-2\rparen} \end{gathered}$

Find two points to the right

$\begin{gathered} when\text{ x=3} \\ y=3^2-6 \\ y=9-6=3 \\ when\text{ x=2} \\ y=2^2-6 \\ y=-2 \\ points\text{ are ;\lparen3,3\rparen and \lparen2,-2\rparen} \end{gathered}$

Plot the graph showing all points

Note;

$-\sqrt{6}=-2.449$