Question

6 points

What is the equation of a parabola with a vertex (-3,-3) that passes
through the point (-2,-5)? Your answer should look like this: y=-3(x+4)^2+2
do not put any spaces
in
your answer. *

Answer 1

`y=-2\,(x+3)^2-3`

Explanation:

Notice that they are asking you to write the equation of the parabola in vertex form, that is using the coordinates of the vertex
`(x_v,y_v)` in the expression:

`y-y_v=a\,(x-x_v)^2\\y=a\,(x-x_v)^2+y_v`

we can start by directly replacing the given vertex coordinates (-3, -3) in the expression, and then using the extra info on the point the parabola goes through in order to find the parameter
`a`:

`y=a\,(x-x_v)^2+y_v\\y=a\,(x+3)^2+(-3)\\y=a\,(x+3)^2-3\\-5=a\,(-2+3)^2-3\\-5=a\,(1)-3\\a=-5+3\\a=-2`

So, now we can write the full expression for the parabola:

`y=a\,(x+3)^2-3\\y=-2\,(x+3)^2-3`