Creating a Quadratic Equation Based off a Word Problem

Question

A local party supply company notices that their maximum profit is reached when they sell 80 balloons and they earn $60 of profit, When they sell 50 balloons they earn $33 of profit. Write a quadratic equation in vertex form to represent their profit

Answer 1

f(x) = ax² + b

 

60 = a(80)² + b

33 = a(50)² + b

 

Solve for a, then determine b.

Convert into vertex form.