Question

What is the equation of the parabola that has a vertex at `(56, -2)` and passes through point `(53,-9)`?

Answer 1

`y = -7/9 (x-56)^2 -2`

Explanation:

The general form of the equation is

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

Given `color(blue)(h = 56), color(green)(k = -2)`

`color(red)(x = 53) , color(purple)(y = -9)`

Substitute into the general form of the parabola

`color(purle)(-9) = a((color(red)(53)-color(blue)(56))^2 color(green)(-2)`
`-9 = a(-3)^2-2`

`-9 = 9a -2`

Solve for `a`

`-9 + 2 = 9a`

`-7 = 9a`

`-7/9= a`

The equation for parabola with the given condition will be

graph{y= -7/9 (x-56)^2 -2 [-10, 10, -5, 5]}