Find the equation for a parabola with given vertex and point.

[TonyC]

Vertex (-5,5) point (-3,17)

Equation for the parabola with the given vertex that passes through the given point.

I am stumped! Please help

 

[daveed]

well, look at this
you have a quadratic of the form ax^2+bx+c
so you have two points
so plug in y and x in for those two points:

5=25a-5b+c
and
17=9a-3b+c

but they also tell you that (-5, 5) is the vertex
which means that there, the solution only has one root; meaning that the x coordinate is equal to -b/2a
so then you have
-5=-b/2a

i think you should be able to solve for this now. perhapsably.

 

[TonyC]

Using what is provided, I have come up with:

y=3(x+5)^2+5

 

[Galileo]

Using what is provided, I have come up with:

y=3(x+5)^2+5

Great. This is always the most insightful way to write the equation of a parabola.
As a check, you can easily see the vertex is at (-5,5). Putting x=-3 gives y=3(2^2)+5=17.