Question

Give an example of a quadratic function has a maximum value. Explain how you know it has a maximum algebraically

Answer 1

y = -x²

Explanation:

The simplest quadratic I can think of is

y = -x²

It must have a maximum because as

x ⟶ -∞, y ⟶ -∞ and as

x ⟶ +∞, y ⟶ -∞.

There must be a maximum somewhere between the two extremes.