Question

What is the range of the function `y=2x^2 +32x - 4`?

Answer 1

`y>=-132`

Explanation:

This a quadratic function with positive leading coefficient so it has a minimum value at its vertex. The vertex of `y=ax^2+bx+c` is `(h,k)` where `h=-b/(2a)` and `k` is found by substitution.

For the given function `h=-32/(2*2)=-32/4=-8`.

Find `k` by substitution:

`k= 2(-8)^2+32(-8)-4`

`k= 128-256-4`
`k=-132`

Since the minimum is `(-8,-132)` and there is no maximum value, the range of the function is `y>=-132`.