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Drawing quadratic graphs practice questions with answers

Foundation and Higher · Grade 5 · Non-calculator

A second set of drawing quadratic graphs questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

On the curve y=x^2-9, work out the value of y when x=4.

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Answer: 7

  1. Substitute x = 4: 4^2 - 9.
  2. Calculate: 16 - 9 = 7.
  • Method (1): Substitute x = 4: 4^2 - 9.
  • Accuracy (1): Calculate: 16 - 9 = 7.

Question 2 Easy

On the curve y=x^2+3, work out the value of y when x=2.

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Answer: 7

  1. Substitute x = 2: 2^2 + 3.
  2. Calculate: 4 + 3 = 7.
  • Method (1): Substitute x = 2: 2^2 + 3.
  • Accuracy (1): Calculate: 4 + 3 = 7.

Question 3 Medium

Find the roots of the curve y=x^2-25.

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Answer: -5 or 5

  1. Set y = 0: x^2 = 25.
  2. Find x-intercepts: x = -5 or 5.
  • Method (1): Set y = 0: x^2 = 25.
  • Accuracy (1): Find x-intercepts: x = -5 or 5.

Question 4 Medium

Find the roots of the curve y=x^2-1.

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Answer: -1 or 1

  1. Set y = 0: x^2 = 1.
  2. Take square roots: x = -1 or 1.
  • Method (1): Set y = 0: x^2 = 1.
  • Accuracy (1): Take square roots: x = -1 or 1.

Question 5 Hard

Find the x-values where the curve y=(x-1)(x-4) crosses the x-axis.

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Answer: 1 or 4

  1. Set y = 0: (x-1)(x-4) = 0.
  2. Crossings: 1 or 4.
  • Method (1): Set y = 0: (x-1)(x-4) = 0.
  • Accuracy (1): Crossings: 1 or 4.

Question 6 Hard

Find the x-values where the curve y=(x-2)(x-5) crosses the x-axis.

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Answer: 2 or 5

  1. Set y = 0: (x-2)(x-5) = 0.
  2. Crossings: 2 or 5.
  • Method (1): Set y = 0: (x-2)(x-5) = 0.
  • Accuracy (1): Crossings: 2 or 5.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

Find the x-values where the curve y=(x-3)(x-7) crosses the x-axis.

Show answer

Answer: 3 or 7

  1. Set y = 0: (x-3)(x-7) = 0.
  2. Solve x - 3 = 0 to get x = 3, and x - 7 = 0 to get x = 7.
  • Method (1): Sets y = 0, or x - 3 = 0, or x - 7 = 0
  • Accuracy (1): 3 and 7

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

How do you find a y-value on y = x^2 + c for a given x?

  1. Square x then add c
  2. Add x and c then square
  3. Multiply x by c
Show answer

Square x then add c Order of operations requires squaring x before adding c.

Check 2

On y = x^2 - 4, what is the value of y at x = 3?

  1. 5
  2. 9
  3. -4
Show answer

5 3^2 - 4 = 9 - 4 = 5.

Check 3

On y = x^2 + 1, what is the value of y at x = 3?

  1. 10
  2. 9
  3. 4
Show answer

10 3^2 + 1 = 9 + 1 = 10.

Check 4

What are the roots of the curve y = x^2 - 4?

  1. -2 or 2
  2. 4
  3. 0 or 4
Show answer

-2 or 2 x^2 = 4, so x = -2 or 2.

Check 5

What are the roots of the curve y = x^2 - 9?

  1. -3 or 3
  2. 9
  3. 0 or 9
Show answer

-3 or 3 x^2 = 9, so x = -3 or 3.

Check 6

What is the y-intercept of the curve y = x^2 - 4?

  1. -4
  2. 0
  3. 4
Show answer

-4 When x = 0, y = -4.

Check 7

What is the y-intercept of the curve y = x^2 + 3?

  1. 3
  2. 0
  3. -3
Show answer

3 When x = 0, y = 3.

Check 8

Where does the curve y = (x-2)(x-3) cross the x-axis?

  1. 2 or 3
  2. 5
  3. -2 or -3
Show answer

2 or 3 At y = 0, x - 2 = 0 or x - 3 = 0.

Check 9

Where does the curve y = (x-1)(x-4) cross the x-axis?

  1. 1 or 4
  2. 5
  3. -1 or -4
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1 or 4 At y = 0, x - 1 = 0 or x - 4 = 0.

Check 10

What is a root of a quadratic curve?

  1. An x-value where the curve crosses the x-axis
  2. The turning point
  3. The y-intercept
Show answer

An x-value where the curve crosses the x-axis Roots are the solutions to y = 0.

Check 11

At what x-value does the y-intercept always occur?

  1. x = 0
  2. x = 1
  3. y = 0
Show answer

x = 0 The y-axis is the line x = 0.

Check 12

Why does y = x^2 - a have two roots when a > 0?

  1. Positive numbers have both a positive and negative square root
  2. Quadratic curves always cross twice
  3. Every curve has symmetry
Show answer

Positive numbers have both a positive and negative square root Square roots can be positive or negative.

Check 13

On y = x^2 - 9, what is the value when x = 4?

  1. 7
  2. 16
  3. -9
Show answer

7 4^2 - 9 = 16 - 9 = 7.

Check 14

What are the roots of y = x^2 - 16?

  1. -4 or 4
  2. 16
  3. 0 or 16
Show answer

-4 or 4 x^2 = 16, so x = -4 or 4.

Check 15

Where does the curve y = (x-2)(x-5) cross the x-axis?

  1. 2 or 5
  2. 7
  3. -2 or -5
Show answer

2 or 5 At y = 0, x = 2 or x = 5.

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