A company is selling books. they need to know how much to sell each book for max profit. We are given: At $20 per book they sell 17,800. At $15 per book they sell 22,960. Their cost per book is $4.90. What price should they sell at to get max profit?

I found the slope and then linear equation using those numbers (-1/1032). as well as the y-intercept (37.25)

I know i need to now make it a quadratic equation to find the vertex for max profit. ax^2+bx+c and i know a will be negative. But i don't know what numbers to plug into which parts of the equation. Meaning: what is a, b , c and x? which variables represent cost, price, quantity, etc?

i got slope as -1/1032. so i think for every dollar the price decreases they sell 1032 more books. y-intercept is 37.25. the price when there is zero demand for books.

I'm stuck on what numbers to put into quadratic equation now.

please help, thanks