Question

What is the equation for a parabola if the vertex is at (5,4) and goes through the point (3,-8)

Answer 1

`y=-3(x-5)^2+4`

Explanation:

Hi there!

Given the vertex of a parabola and a point, it's easiest to organize the equation in vertex form:

`y=a(x-h)^2+k` where the vertex is located at
`(h,k)` and a is a numerical value

1) Plug the vertex into the equation

`y=a(x-h)^2+k`

Plug in the vertex (5,4)

`y=a(x-5)^2+4`

2) Solve for a

`y=a(x-5)^2+4`

Plug in the given point (3,-8) and solve for a

`-8=a(3-5)^2+4\\-8=a(-2)^2+4\\-8=4a+4`

Subtract 4 from both sides

`-8-4=4a+4-4\\-12=4a`

Divide both sides by 4

`(-12)/(4) = (4a)/(4) \\-3=a`

Therefore, a=-3. Plug this back into
`y=a(x-5)^2+4`:

`y=-3(x-5)^2+4`

I hope this helps!