A quadratic graph is a parabola
gives a U-shape (a > 0) or ∩-shape (a < 0). It crosses the x-axis at the solutions of and the y-axis at .
Completing the square gives the turning point
Writing shows the turning point is at — the minimum (or maximum) of the curve.
Solve by reading roots from the graph
Where the curve crosses the x-axis (y = 0) are the solutions; symmetry puts the turning point exactly halfway between the two roots.
Drawn from real examiner reports.
Not drawing a sketch when solving a quadratic inequality
Students who drew a sketch had a much better chance of writing the correct final inequality (single region vs two distinct regions); those who did not often gave the wrong direction.
"Reverse-engineering" factors from a calculator
Reading factors off a calculator gave forms like (x + 2.1)(x − 1) that do not expand back to the given quadratic, and scored nothing where algebraic working was required.
Misreading the graph scale
Marks were lost reading values off the axes when each square was not one unit — always check the scale before reading a root or a turning point.
Plot a smooth curve and find symmetry
Join plotted points with a single smooth curve (never ruled segments) and use the line of symmetry to locate the turning point.
is a parabola: a U-shape if , an ∩-shape if .
Where does y = x² + bx + c cross the y-axis?
The curve is drawn. Find the coordinates of the points where it crosses the x-axis.
