Question

Find an equation of the parabola that has the indicated vertex and whose graph passes through the given point
Vertex: ( 2, -1) ; point: ( 4, -3)

Answer 1

Do you know if the parabola has a vertical or horizontal axis?

Answer 2

no I don't

Answer 3

Do you expect it to look like
(y-k)=a(x-h)^2, or
(x-h)=a(y-k)^2?

Answer 4

I am not sure what it is suppose to look like....I just need to find an equation....I don't know how to solve the problem

Answer 5

There are two solutions.
The equation could be of the form
(y-k)=a(x-h)^2, or
(x-h)=a(y-k)^2
where (h,k) is the location of the vertex (2,-1), and
a is a parameter to be found.

Answer 6

Thank you but how do you work out the problem

Answer 7

Substitute (h,k) into the equations, and the given point into the x- and y-values to solve for a.
You can choose one of the two forms, or do both.

Answer 8

Where do I put the point values of (4, -3) in the equation?

Answer 9

For example, if a parabola has a vertex (3,5) and passes through (5,9), then
h=3, k=5, and put x=4 and y=9 to find a.
For vertical axis, we use (y-k)=a(x-h)^2 to get
(9-5)=a(5-3)^2
solving for a gives a=1, so the equation is
(y-5)=(x-3)^2

Answer 10

* x=5

Answer 11

how did u get a=1?

Answer 12

(9-5)=a(5-3)^2
4=a(2^2)
4=4a
a=1