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

Question

asked Sep 17, 2022 90.4k views

1 Answer

Moethata · Answer 1 · 2022-09-21T17:24:07+0000

Answer:

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!