What is important to know about Quadratic graphs?

Quadratic graphs are parabolas — symmetrical U or ∩ shapes.

What is important to know about Quadratic graphs?

The graph crosses the y-axis where x = 0 (substitute x = 0 to find the y-intercept).

What is important to know about Quadratic graphs?

It crosses the x-axis where y = 0 (the roots of the quadratic).

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Algebra · Foundation & Higher

Quadratic graphs

Q: What are common mistakes with Quadratic graphs?

Arithmetic errors when substituting negative x values (remember (−2)² = 4, not −4).

Q: What are common mistakes with Quadratic graphs?

Drawing a V-shape instead of a smooth curve — quadratics are smooth parabolas.

Q: What exam tips are there for Quadratic graphs?

Always substitute carefully, especially with negative values — show each substitution step.

Q: What exam tips are there for Quadratic graphs?

Plot at least 5–7 points and join with a smooth curve, not straight lines.

A quadratic graph has the equation y = ax² + bx + c and produces a parabola (U-shape if a > 0, ∩-shape if a < 0). You need to draw them by completing a table of values and identify key features.

Revising quadratic graphs the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Quadratic graphs GCSE” on the site for the complete guide.

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Key facts to remember

1Quadratic graphs are parabolas — symmetrical U or ∩ shapes.
2The graph crosses the y-axis where x = 0 (substitute x = 0 to find the y-intercept).
3It crosses the x-axis where y = 0 (the roots of the quadratic).
4The turning point (vertex) lies on the line of symmetry x = −b/(2a).
5If a > 0, the parabola opens upward (minimum point); if a < 0, it opens downward (maximum point).

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Formulas

Line of symmetry

x = −b / (2a)

For y = ax² + bx + c

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Worked examples

Example 1

Complete a table of values for y = x² − 3x + 2 for x = 0 to 4, and state the roots.

Working

x = 0: y = 0 − 0 + 2 = 2
x = 1: y = 1 − 3 + 2 = 0
x = 2: y = 4 − 6 + 2 = 0
x = 3: y = 9 − 9 + 2 = 2
x = 4: y = 16 − 12 + 2 = 6
Roots (where y = 0): x = 1 and x = 2

AnswerRoots at x = 1 and x = 2

Example 2

Find the coordinates of the turning point of y = x² − 4x + 1.

Working

Line of symmetry: x = −(−4) / (2 × 1) = 4/2 = 2
y at x = 2: y = 4 − 8 + 1 = −3
Turning point is (2, −3)

Answer(2, −3)

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Common mistakes

✗Arithmetic errors when substituting negative x values (remember (−2)² = 4, not −4).

✗Drawing a V-shape instead of a smooth curve — quadratics are smooth parabolas.

✗Not plotting enough points to identify the turning point accurately.

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Exam tips

✓Always substitute carefully, especially with negative values — show each substitution step.

✓Plot at least 5–7 points and join with a smooth curve, not straight lines.

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