DRAWING QUADRATIC GRAPHS (EDEXCEL HIGHER) These questions are suitable for Higher Tier students. All questions should be done without a calculator.
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1 GCSE MATHEMATICS KEY TOPIC PRACTICE SHEETS DRAWING QUADRATIC GRAPHS (EDEXCEL HIGHER) These questions are suitable for Higher Tier students. All questions should be done without a calculator.
2 1 (a) Complete the table of values for y = x $ + x 1 x y (b) On the grid below, draw the graph of y = x $ + x 1 for values of x from -4 to 2 (Total for Question 1 is 4 marks) Copyright tutor2u
3 2 (a) Complete the table of values for y = 5 x $ x x y (b) On the grid below, draw the graph of y = 5 x $ x for values of x from -4 to 2 (Total for Question 2 is 4 marks) Copyright tutor2u
4 3 (a) Complete the table of values for f(x) = x $ + 2x 7 x f(x) (b) On the grid below, draw the graph of f(x) for the range 4 x 2 (c) Use your graph to estimate the value of f( 2.5) f 2.5 =. (1) (Total for Question 3 is 5 marks) Copyright tutor2u
5 4 Davina has been given this table of values for y = x $ + 3x 4 x y Davina s teacher has asked her to draw the graph of y = x $ + 3x 4 for values of x from -5 to 1. Davina s graph is shown below. Write down three mistakes with Davina s graph. Mistake Copyright tutor2u
6 Mistake Mistake (Total for Question 4 is 3 marks) Copyright tutor2u
7 5 (a) Complete the table of values for f(x) = x $ + 4x 3 x f(x) (b) On the grid below, draw the graph of f(x) = x $ + 4x 3 for values of x from -1 to 5 (c) Use your graph to estimate the values of x when f(x) = 6 x = and (Total for Question 5 is 6 marks) Copyright tutor2u
8 6 Maya has been given this table of values for y = x $ 4x + 3 x y Maya s teacher has asked her to draw the graph of y = x $ 4x + 3 for values of x from -5 to 1. Maya s graph is shown below. Write down two mistakes with Maya s graph. Mistake Copyright tutor2u
9 Mistake (Total for Question 6 is 2 marks) Copyright tutor2u
10 7 The graph for y = 2x $ + 3x 5 is drawn below. (a) State whether the turning point of this graph is a minimum or a maximum. (b) Find the co-ordinates of this turning point. Estimate each of your answers to one decimal place.... (1) , (Total for Question 7 is 3 marks) Copyright tutor2u
11 8 (a) Is the turning point of the graph for y = x $ + x a minimum or a maximum? Explain your answer (b) What are the co-ordinates of the y-intercept for the graph y = x $ + x? 9 Which of these are correct statements about the graph y = x $ 5x + 1? Tick all correct statements. The co-ordinates of the y-intercept are (0, 1) The turning point is a maximum The turning point is a minimum The graph passes through (3, -8) , (1) (Total for Question 8 is 3 marks) (Total for Question 9 is 3 marks) Copyright tutor2u
12 10 The turning point of the graph y = x $ 6x + 10 is (a, b) a and b are integers. Explain, with the use of a diagram or otherwise, why the turning point of the graph cannot lie between the coordinates (5, 5) and (7, 17). (Total for Question 10 is 3 marks) Copyright tutor2u
13 11 Graphs of the following functions have been drawn on the grid below Functions y = 2x + 5 y = x $ + 6x + 10 y = x $ 4x 3 y = 2 x Each graph has been labelled Graph A, Graph B, Graph C or Graph D. Match each of the functions with its corresponding graph by completing the table below. Graphs Graph A Graph B Graph C Graph D Functions (Total for Question 11 is 3 marks) Copyright tutor2u
14 12 (a) Complete the table of values for y = x(3 x) x y (b) On the grid below, draw the graph of y = x(3 x) for values of x from -2 to 4 Copyright tutor2u
15 (c) By drawing the line y = 2x 2 on the same grid, solve the equations y = 3x x $ y = 2x 2 x =, y = (Total or x =, y = (3) for Question 12 is 7 marks) Copyright tutor2u
16 13 (a) Complete the table of values for y = x $ 3x 1 x y (b) On the grid below, draw the graph of y = x $ 3x 1 for values of x from -1 to 5 Copyright tutor2u
17 The solution to x $ 3x 1 < 2 is a < x < b (c) By drawing the line y = 2 on the same grid, find estimates for the values of a and b. Give your answers to one decimal place. a =. b =. (3) (Total for Question 13 is 7 marks) Copyright tutor2u
18 14 (a) Draw the graph for y = x $ 1 on the grid below for values in the range 3 < x < 3 (4) (b) On the same grid, draw the graph for x $ + y $ = 4 Copyright tutor2u
19 (c) Using your answers to parts (a) and (b), estimate the solutions to the equations x $ + y $ = 4 y = x $ 1 x =, y = or x =, y = (3) (Total for Question 14 is 4 marks) Copyright tutor2u
20 15 (a) Complete the table of values for y = 2x $ 2x 4 x y (b) On the grid below, draw the graph of y = 2x $ 2x 4 for values of x from -2 to 4 Copyright tutor2u
21 Use your graph to answer the following questions (c) Estimate the gradient of the curve at the point (3, 8) (d) Estimate the area enclosed between the curve and the x-axis. You must show all your working out. Gradient =. Area =. (4) (Total for Question 15 is 10 marks) Copyright tutor2u
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