A11AlgebraFoundation & Higher

Quadratic & Other Graphs

Not every graph is a straight line. Quadratics make a U-shaped curve called a parabola, and you should also recognise cubic and reciprocal graphs by their shape.

40 min AQA GCSE Maths

What you'll learn

Plot a quadratic graph from a table of values
Recognise the parabola shape
Read roots and the turning point from a graph
Recognise cubic and reciprocal graphs

Quadratic graphs (parabolas)

A quadratic like $y = x^{2}$ gives a symmetric U-shaped curve. If the $x^{2}$ term is positive the curve opens upward (a valley); if negative it opens downward (a hill). Build a table of values, then plot and join with a smooth curve.

1The curve crosses where

y = 0

x^{2} - 4 = 0

x^{2} = 4

, so

x = 2

x = - 2

Answer

x = 2

and

x = - 2

Tip — Join quadratic points with a smooth curve — never with straight line segments.

Other graph shapes

A $cubic$ ( $y = x^{3}$ ) has an S-shape. A $reciprocal$ ( $y = \frac{1}{x}$ ) has two separate curves and never touches the axes. Recognising these shapes is a common exam question.

Remember these

y = x^{2}

Parabola — U-shaped curve.

y = \frac{1}{x}

Reciprocal — two curves, never touches the axes.

Watch out for these

Joining quadratic points with straight lines.

Use a single smooth curve.

Forgetting a parabola is symmetric.

The two sides mirror each other about the turning point.

Key takeaways

Quadratics make a U-shaped parabola (smooth curve).
Roots are where the curve crosses the x-axis (y = 0).
Know the cubic (S-shape) and reciprocal (two curves) shapes.

Test yourself

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