Question

What is the equation of the parabola that has a vertex at `(-8, 5)` and passes through point `(-18,32)`?

Answer 1

When doing problems such as this one, it is simplest to write the equation using the formula y = a`(x - p)^2` + q.

Explanation:

In y = a`(x - p)^2` + q. the vertex is at (p, q). Any point (x, y) that lies on the parabola can be plugged into x and y in the equation. Once you have four out of the five letters in the equation, you can solve for the fifth, which is a, the characteristic that influences the parabola's width in comparison with y = `x^2` and its opening direction (downward if a is negative, upwards if a is positive)

32 = a`(-18 - (-8))^2` + 5
32 = a`(-10)^2` + 5
32 = 100a + 5
27 = 100a
a = `27/100` or 0.27

y = `27/100` `(x + 8)^2` + 5

Your final equation is y = `27/100` `(x + 8)^2` + 5.

Hopefully you understand now.