Every quadratic function wears the same uniform: $y = ax^2 + bx + c$ — read aloud: y equals a x-squared plus b x plus c. Three coefficients, three jobs. a is welded to the $x^2$ and decides the fold: positive a cups the graph upward (a parabola that could hold water), negative a folds it into a frown. c camps alone at the end and marks the y-intercept — set $x = 0$ and c is the only term left breathing.

b is the subtle one: it slides the vertex off the y-axis, and you will spend this whole chapter negotiating with it. No computing today — this lesson is about READING, and signs are part of the deal. In $y = 3x^2 - 5x + 7$, b is −5, not 5. The sign travels with its term, always.