Question

What is the range of the function f(x)=3x^2+6x-8

Answer 1

The range is [-11, ∞).

Explanation:

f(x)=3x^2+6x-8

This is a parabola which opens upwards.

Convert to vertex form:

= 3(x^2 + 2x) - 8

= 3 [ (x + 1)^2 - 1] - 8

= 3(x + 1)^2 - 3 - 8

= 3(x + 1)^2 - 11.

The minimum value is -11 so the range is [-11, ∞).

Answer 2

[-11,∞),{yiy≥-11}