Question

What is the equation of the parabola that has a vertex at `(0, 8)` and passes through point `(2,32)`?

Answer 1

We must first analyze vertex form.

Explanation:

Vertex form is `y = a(x - p)^2 + q`. The vertex is at (p, q). We can plug the vertex in there. The point (2, 32) can go into (x, y). After this, all we must do is solve for a, which is the parameter that influences the width, size and direction of opening of the parabola.

`32 = a(2 - 0)^2 + 8`

`32 = 4a + 8`

32 - 8 = 4a#

`24 = 4a`

`6 = a`

The equation is `y = 6x^2 + 8`

Practice exercises:

1. Find the equation of a parabola that has a vertex at (2, -3) and that passes through (-5,-8).

Challenge problem:

What is the equation of a parabola that pass through the points `(-2, 7), (6, -4) and (3,8)`?

Good luck!