The given equation of the parabola is:
[tex]y=(x+2)^2-3[/tex]
It is required to plot five points: the vertex, two points to the right of the vertex, and two points to the left of the vertex. Then, it is also required to click on the graph-a-function button to graph the parabola.
Recall that the vertex of a parabola whose equation is written in vertex form,
y=(x-h)²+k is given as:
[tex]Vertex=(h,k)[/tex]
Rewrite the given equation as:
[tex]y=(x-(-2))^2+(-3)[/tex]
It follows that h=-2 and k=-3.
Hence, the vertex of the parabola is (-2,-3).
Find two points to the left of the vertex.
Substitute x=-3 into the equation:
[tex]\begin{gathered} y=(-3+2)^2-3 \\ \Rightarrow y=(-1)^2-3=1-3=-2 \end{gathered}[/tex]
A point is (-3,-2).
Substitute x=-4 into the equation:
[tex]\begin{gathered} y=(-4+2)^2-3 \\ \Rightarrow y=(-2)^2-3 \\ \Rightarrow y=4-3=1 \end{gathered}[/tex]
Another point to the left of the vertex is (-4,1).
Find two points to the right of the vertex.
Substitute x=-1 into the equation:
[tex]\begin{gathered} y=(-1+2)^2-3 \\ \Rightarrow y=(1)^2-3=1-3=-2 \end{gathered}[/tex]
A point to the right is (-1,-2).
Substitute x=0 into the equation:
[tex]\begin{gathered} y=(0+2)^2-3 \\ \Rightarrow y=(2)^2-3=4-3=1 \end{gathered}[/tex]
Another point to the right is (0,1).
Plot the points as shown:
Click the graph-a-function button to get the required graph:
