Question

What is the range of the function f(x) =5x^2−20x+12
?

Answer 1

f(x) = 5x^2 − 20x + 12 = 5(x^2 − 4x) + 12 = 5[(x − 2)^2 − 4] + 12 = 5(x − 2)^2 − 8.

Since 5(x − 2)^2 ≥ 0, the minimum value is −8 at x = 2. Range: [−8, ∞).