Question

What is the equation of the parabola that has a vertex at `(4, -3)` and passes through point `(31,-4)`?

Answer 1

For problems like this, use vertex form `y = a(x - p)^2 + q`, where `(x, y)` is the point on the function, `(p, q)` is the vertex, and `a` influences the breadth of the parabola. We will be solving for `a`.

`-4 = a(31 - 4)^2 - 3`

`-4 = 729a - 3`

`-1 = 729a`

`-1/729 = a`

Hence, the equation of the parabola is `y = -1/729(x - 4)^2 - 3`

Hopefully this helps!