Knowing WHEN a business peaks is half a mark. The paper wants the peak itself, and that is the vertex's other coordinate: $k = c - \dfrac{b^2}{4a}$ — k equals c minus b-squared over four a. $k$ is the y-coordinate of the vertex, the model's greatest value when a is negative and its least when a is positive; $a$, $b$ and $c$ are the same three coefficients, signs attached, and this time all three are needed.

You never have to trust the formula blind. Find $h = -\dfrac{b}{2a}$ first, substitute it back into the model, and the arithmetic rebuilds $k$ in three lines — that substitution IS where $c - \dfrac{b^2}{4a}$ comes from. This lesson runs it as a two-step deliberately: locate the turn, then evaluate there. Every optimization question you will meet for the rest of the year has that same shape, right through to Lagrange multipliers.

The sign trap worth naming: with a negative, dividing by $4a$ makes the correction term negative, so SUBTRACTING it raises the peak above c. That feels wrong the first three times and is right every time. Sanity check: for a profit model, k should come out a plausible amount of money — if it lands below c on a downward parabola, a sign got away from you.