Question

What is the vertex of `y=3x^2+12x - 15`?

Answer 1

Complete the square to convert to vertex form.

Explanation:

y = `3x^2` + 12x - 15
y = 3(`x^2` + 4x + n - n) - 15
n = `(b/2)^2`
n = 4
y = 3(`x^2` + 4x + 4 - 4) - 15
y = 3(`x^2` + 4x + 4) - 12 - 15
y = 3(`x^2` + 4x + 4) - 27
y = 3`(x + 2)^2` - 27

In the form y = a`(x - p)^2` + q, the vertex can be found at (p, q). So, the vertex is (-2, -27).

Hopefully my explanation helps!