[tex]\text{ y = 3(x+1)}^2-2[/tex]
To graph the function, we need to get a set of coordinates of points (x, y) that will allow us to plot the points on the graph.
[tex]\begin{gathered} \\ y=\text{3(x+1)}^2-2 \\ \text{When x=-3,} \\ y=3(-3+1)^2-2=3(-2)^2-2 \\ y=10 \\ \text{ (-3, 10) is a point on the graph} \end{gathered}[/tex]
when x = -2,
[tex]\begin{gathered} \text{ y = 3(-2+1)}^2-2 \\ y=3(-1)^2-2\text{ = 3(1)-2} \\ y=\text{ 1} \\ \text{ (-2, 1) is a point on the graph} \end{gathered}[/tex]
when x = -1
[tex]\begin{gathered} \text{ y=3(-1+1)}^2-2 \\ y=3(0)^2-2 \\ y=-2 \\ (-1,\text{ -2) is a point on the graph} \end{gathered}[/tex]
when x = 0
[tex]\begin{gathered} \text{y=3(0+1)}^2-2 \\ y=3(1)^2-2 \\ y=3-2 \\ y=1 \\ (0,\text{ 1) is a point on the graph} \end{gathered}[/tex]
When x = 1
[tex]\begin{gathered} \text{y=3(1+1)}^2-2 \\ y=3(2)^2-2 \\ y=3(4)-2\text{ = 12-2} \\ y=10 \\ (1,\text{ 10) is a point on the graph} \end{gathered}[/tex]
The set of points on the graph are ( -3, 10) , (-2, 1), (-1, -2), (0, 1), (1, 10). These points allow us to draw the graph of the function as drawn in the picture uploaded above
