Please help me with this question

Question

Find the largest value q such that the function f : (−∞, q] → R given by f(x) = −x 2 + 2x + 8 is injective.

Answer 1

Injective means 1-1. ie f(x) = f(y) implies x = y.

f(x) is a quadratic so you need to choose q so that x = q is the axis of symmetry.

so q = x coordinate of vertex where q = -b/2a

and f(x) = ax² + bx + c