Quadratic Functions and Equations in One Variable · 1.1.3
Effect of a, b, c on graphs
Students explore how each coefficient shapes the parabola: a controls whether it opens upward or downward and how wide or narrow it is, b (together with a) affects the position of the turning point sideways, and c fixes where the graph crosses the y-axis.
The official learning standard (1.1.3)
“Investigate and make generalisation about the effect of changing the values of a, b and c on graphs of quadratic functions, f(x) = ax² + bx + c.”
What it means
Students explore how each coefficient shapes the parabola: a controls whether it opens upward or downward and how wide or narrow it is, b (together with a) affects the position of the turning point sideways, and c fixes where the graph crosses the y-axis.
How it is examined
This is mainly tested in Paper 1 through matching graphs to their equations or predicting how a graph changes when a coefficient increases, decreases, or changes sign. Paper 2 may ask for a short explanation as part of a graph-sketching question.
Worked example
State the effect on the graph of f(x) = 2x² + bx + 3 when the value of a is changed from 2 to −2, while b and c remain unchanged.
- When a = 2 (positive), the parabola opens upward with a minimum turning point.
- When a = −2 (negative), the parabola opens downward with a maximum turning point instead.
- Since |a| = 2 in both cases, the width of the parabola stays the same; only the direction it opens changes.
- The y-intercept, c = 3, is unchanged because c does not depend on a.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What happens to the graph if a becomes negative?
The parabola flips direction: instead of opening upward with a minimum point, it opens downward with a maximum point. The position of the turning point may also shift if b changes, but the flip in direction is caused purely by the sign of a.
Does changing c move the whole graph up or down?
Yes. Increasing c shifts the whole parabola upward, and decreasing c shifts it downward, without changing its shape or width.
The value of c is always the y-coordinate where the graph crosses the y-axis, since f(0) = c.
How does b affect the graph?
Together with a, b determines the horizontal position of the turning point, given by the axis of symmetry x = −b/(2a). Changing b alone shifts the parabola sideways and slightly changes the y-intercept's neighbourhood, but the overall shape stays the same.