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Quadratic graphs questions and answers

The graph of y=ax2+bx+cy = ax^2 + bx + c is a U-shaped curve (a parabola), upside down if aa is negative. It crosses the y-axis at cc, crosses the x-axis at the roots (where y=0y = 0), and is symmetrical about a vertical line through its turning point, halfway between the roots.

8 questions · Foundation and Higher tier · Every answer is checked as you type it, with a full worked solution. Updated .

Start the questions Quadratic equations: lesson and examples

Where quadratic graphs comes up

GCSE (AQA, Edexcel, OCR)Foundation and Higher: identify and interpret roots, intercepts and turning points of quadratic functions graphically. Higher only: deduce turning points by completing the square.
Cambridge IGCSE (0580)Core and Extended: draw and interpret graphs of quadratic functions and find roots graphically (Core doesn't need turning points). Extended: sketch quadratics, including turning points.

The method

  1. y-intercept: put x = 0 (it's the number c).
  2. Roots: solve y = 0.
  3. Line of symmetry: halfway between the roots.
  4. Turning point: substitute the line of symmetry's x value, or complete the square: y = (x + p)² + q has turning point (−p, q).

Quadratic graphs questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

Where does y=x2−4y = x^2 - 4 cross the y-axis? Give the y value.

Question 2Warm-upFoundation

Find the roots of y=x2−6x+8y = x^2 - 6x + 8 (where it crosses the x-axis).

Exam-style

Question 3Exam-styleFoundation

Complete the table of values for y=x2+2x−3y = x^2 + 2x - 3: what is yy when x=−2x = -2?

Question 4Exam-styleFoundation

Write down the coordinates of the turning point of y=x2−6x+8y = x^2 - 6x + 8.

Question 5Exam-styleFoundation

y=x2−2x−8y = x^2 - 2x - 8 has roots x=−2x = -2 and x=4x = 4. What is its line of symmetry? Type the x value.

Question 6Exam-styleHigher

By completing the square, find the turning point of y=x2+4x+7y = x^2 + 4x + 7.

Challenge

Question 7ChallengeHigher

Does the graph of y=x2+4x+7y = x^2 + 4x + 7 cross the x-axis?

Question 8ChallengeHigher

Find the turning point of y=2x2−8x+3y = 2x^2 - 8x + 3.

Common mistakes

  • Confusing the roots with the y-intercept.
  • Squaring negative x values wrongly in a table: (−2)² = 4.
  • Getting the sign of the turning point's x-coordinate wrong.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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