The parent function for quadratic equations is as followed:
[tex]y=a(bx-h)^2+k[/tex]
where a for vertical stretches, b is for horizontal stretches, h is the x value of the vertex, and k is the y value of the vertex.
The vertex of the is (-3, -2), so we can write the first part of the equation:
[tex]y=a(bx+3)^2-2[/tex]
To determine if the graph has any stretches, we can check how changes to the x coordinate affect the y value. If there are no stretches, as the x coordinate moves away from the vertex, the y coordinate should be x^2 from the vertex. If we test with a couple points on the graph, wee see that this is true, so there are no stretches. The answer is:
[tex]y=(x+3)^2-2[/tex]
