Robinson Tuition
Grade 4 · Foundation and Higher · free GCSE maths worksheet

Plotting quadratic graphs

Table of values and smooth curve.

13 original questions, 50 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Complete the table of values for y = x2 - 2

x-2-1012
y2-22
2 marks
Show answer
x = -1) -1 x = 1) -1
2

Complete the table of values for y = x2 + 3

x-3-2-10123
y73412

Write down the equation of the line of symmetry of the graph.

3 marks
Show answer
a) x = -3: 12, x = -1: 4, x = 2: 7 b) x = 0
3

The diagram shows the graph of y = x2 - 2x - 3

  1. Write down the coordinates of the point where the graph crosses the y-axis.
  2. Write down the solutions of x2 - 2x - 3 = 0
  3. Write down the coordinates of the turning point of the graph.
−3−2−112345−5−4−3−2−1123456Oxy
3 marks
Show answer
a) (0, -3) b) x = -1 and x = 3 c) (1, -4)
4
  1. Complete the table of values for y = x2 - 3x + 1
    x-101234
    y51-1
  2. On the grid, draw the graph of y = x2 - 3x + 1 for values of x from -1 to 4
−11234−2−1123456Oxy
4 marks
Show answer
a (x = 1)) -1 a (x = 3)) 1 a (x = 4)) 5 b) correct smooth parabola through (-1, 5), (0, 1), (1, -1), (2, -1), (3, 1), (4, 5)
5

Complete the table of values for y = x2 − x − 2

x-2-10123
y4-204
  1. Complete the table.
  2. Use your table to write down the two solutions of x2 − x − 2 = 0.
  3. Work out the value of y when x = 1.5.
4 marks
Show answer
a) x = -1: 0, x = 1: -2 b) x = -1 and x = 2 c) -1.25
6
  1. Complete the table of values for y = 6 - x2
    x-3-2-10123
    y-355-3
  2. Write down the coordinates of the maximum point of the graph of y = 6 - x2
  3. Use the table to write down the two consecutive whole numbers that the positive solution of 6 - x2 = 0 lies between.
4 marks
Show answer
a (x = -2)) 2 a (x = 0)) 6 a (x = 2)) 2 b) (0, 6) c) between 2 and 3
7
  1. Complete the table of values for y = x2 + 2x - 8
    x-4-3-2-1012
    y0-5-9-5
  2. Use the table to write down the solutions of x2 + 2x - 8 = 0
  3. Write down the equation of the line of symmetry of the graph of y = x2 + 2x - 8
4 marks
Show answer
a (x = -2)) -8 a (x = 0)) -8 a (x = 2)) 0 b) x = -4 and x = 2 c) x = -1
8
  1. Complete the table of values for y = x2 - 4x
    x-1012345
    y50-35
  2. On the grid, draw the graph of y = x2 - 4x for values of x from -1 to 5
  3. Write down the coordinates of the turning point of the graph.
−112345−5−4−3−2−1123456Oxy
5 marks
Show answer
a (x = 1)) -3 a (x = 2)) -4 a (x = 4)) 0 b) correct smooth parabola through (-1, 5), (0, 0), (1, -3), (2, -4), (3, -3), (4, 0), (5, 5) c) (2, -4)
9

Here is a table of values for y = x2 − 6x + 5

x0123456
y50-405
  1. Complete the table.
  2. Write down the equation of the line of symmetry and the coordinates of the turning point of the graph.
  3. Work out the value of y when x = 3.5.
4 marks
Show answer
a) x = 2: -3, x = 4: -3 b) x = 3; (3, -4) c) -3.75
10

Here is a table of values for y = 2x2 + x − 6

x-3-2-1012
y0-64
  1. Complete the table.
  2. Use the table to write down one solution of 2x2 + x − 6 = 0.
  3. Show that x = 1.5 is also a solution of 2x2 + x − 6 = 0.
4 marks
Show answer
a) x = -3: 9, x = -1: -5, x = 1: -3 b) x = -2 c) shown
11
  1. Complete the table of values for y = 2x2 - 3
    x-2-1012
    y5-1
  2. Write down the coordinates of the turning point of the graph of y = 2x2 - 3
  3. Use the table to write down the two consecutive whole numbers that the positive solution of 2x2 - 3 = 0 lies between.
5 marks
Show answer
a (x = -1)) -1 a (x = 0)) -3 a (x = 2)) 5 b) (0, -3) c) between 1 and 2
12

Here is a table of values for y = x2 − 4x + 3

x-1012345
y83-138
  1. Complete the table.
  2. Write down the coordinates of the turning point.
  3. Use the table to solve x2 − 4x + 3 = 0.
  4. Work out the value of y when x = 6.
4 marks
Show answer
a) x = 1: 0, x = 3: 0 b) (2, -1) c) x = 1 and x = 3 d) 15
13

A ball is thrown upwards. Its height, h metres, after t seconds is given by h = 12t − 3t2

t01234
h099
  1. Complete the table.
  2. Write down the greatest height of the ball and when it reaches it.
  3. Work out the height of the ball after 1.5 seconds.
  4. After how many seconds does the ball hit the ground?
4 marks
Show answer
a) t = 2: 12, t = 4: 0 b) 12 m after 2 seconds c) 11.25 m d) 4 seconds

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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