Quadratic Functions and Equations in One Variable

Parabola

The U-shaped curve of a quadratic function; it opens upward if a is positive and downward if a is negative.

EnglishParabola
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How it is used

The graph of y = x² − 4x + 3 is a parabola opening upward (a = 1 > 0); it cuts the x-axis at x = 1 and x = 3 and has its lowest point at (2, −1).

Where it shows up in SPM

The shape of every quadratic graph (Form 4). Paper 2 asks you to sketch or interpret parabolas, marking the x-intercepts (roots), the y-intercept, and the turning point, and to state where the curve is above or below the x-axis.

Don't confuse it with

HyperbolaA parabola is one connected U-shaped curve from y = ax² + bx + c, while the graph of an inverse variation y = k/x is a hyperbola in two separate branches.
Axis of symmetryThe parabola is the curve itself; the axis of symmetry is the vertical line that splits that curve into two mirror halves.

Open the chapter: Quadratic Functions and Equations in One Variable →

Frequently asked questions

How do I know if a parabola opens up or down?

Look at the coefficient a. If a is positive the parabola opens upward and has a minimum turning point; if a is negative it opens downward and has a maximum turning point.

For y = −2x² + x + 3, a = −2, so it opens downward.

What key points should I mark when sketching a parabola?

Mark the roots where it crosses the x-axis, the y-intercept (the value of c), and the turning point. Also show whether it opens up or down.

These few points let you draw an accurate sketch and earn the method marks in Paper 2.

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