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The Robert Smyth School Mathematics Faculty Y10 Topic 9 Quadratics Innovation & excellence Name: HW1 – Grade C Drawing Quadratic Graphs 1. (a) Complete the table of values for y = x2 – 3 x –3 y –2 –1 0 1 1 –2 –3 –2 2 Teacher Assessment 3 6 ..................................................................................................................................... (1) (b) On the grid draw the graph of y = x2 – 3 for values of x from –3 to +3 y 6 5 4 3 2 1 –3 –2 –1 O 1 2 x 3 –1 –2 –3 –4 (2) (c) Use the graph to solve the equation x2 – 3 = 0 Answer .................................... (2) (d) Write down the values of x at the points where the line y = 2 crosses your graph. ..................................................................................................................................... Answer .............................. and .............................. (2) (Total 7 marks) The Robert Smyth School 1 The Robert Smyth School Mathematics Faculty Y10 Topic 9 Quadratics Innovation & excellence 2. (a) Complete the table for the equation y = x2 – 2x + 2 x –1 0 1 2 3 y (1) (b) On the grid below draw the graph of y = x2 – 2x + 2 for –1 < x < 3. y 5 4 3 2 1 –1 0 1 2 3 4 x (2) (c) Use your graph to find the values of x when y = 3. …….……..……….…..…..……………………………….…………………..…….. …….……..……….…..…..……………………………….…………………..…….. (1) The Robert Smyth School 2 The Robert Smyth School Mathematics Faculty Y10 Topic 9 Quadratics Innovation & excellence 3. (a) Complete this table of values for y = (2 + x)(3 – x) x –2 y –1 0 1 2 3 4 6 6 4 0 4 ……………...........………………………….....……………………………………. ……………...........………………………….....……………………………………. (2) (b) On the grid, draw the graph of y = (2 + x)(3 – x) for values of x from –2 to + 4. y 7 6 5 4 3 2 1 –2 –1 O 1 2 3 4 x –1 –2 –3 –4 –5 –6 –7 (2) (Total 4 marks) The Robert Smyth School 3 The Robert Smyth School Mathematics Faculty Y10 Topic 9 Quadratics Innovation & excellence 4. (a) Complete the table of values for y = 2x2– 5x x –2 –1 0 1 2 y 18 7 0 –3 –2 3 4 12 (1) (b) On the grid below, draw the graph of y = 2x2 – 5x for values of x between –2 and +4. y 18 16 14 12 10 8 6 4 2 –2 –1 O 1 2 3 4 –2 x (2) –4 (c) Write down the value of x for which y has a minimum value. Answer x=..................................................... (1) (Total 4 marks) Success: The Robert Smyth School Target: 4 The Robert Smyth School Mathematics Faculty Y10 Topic 9 Quadratics Innovation & excellence HW2 – Grade B Solving quadratic equations by drawing quadratic graphs 1. (a) Teacher Assessment Complete the table for the graph of y = x2 – 3x + 1. x –1 y 0 1 2 1 –1 –1 3 4 5 ..................................................................................................................................... ..................................................................................................................................... (2) (b) On the grid below, draw the graph of y = x2 – 3x + 1 for values of x from –1 to + 4. y 5 4 3 2 1 –1 1 2 3 4 x –1 –2 (2) (c) Use your graph to solve the equation x2 – 3x + 1 = 0. ..................................................................................................................................... Answer .............................. and ............................... (2) (Total 6 marks) The Robert Smyth School 5 The Robert Smyth School Mathematics Faculty Y10 Topic 9 Quadratics Innovation & excellence 2. (a) Complete the table of values for y = x2 – 4x – 1. x –1 y 0 1 –1 –4 2 3 4 5 –4 –1 4 ...................................................................................................................................... ...................................................................................................................................... (2) (b) On the grid, draw the graph of y = x2 – 4x – 1 for values of x from –1 to +5. y 5 4 3 2 1 –2 –1 O 1 2 3 4 5 6 x –1 –2 –3 –4 –5 –6 (2) (c) Use your graph to solve the equation x2 – 4x – 1 = 0. Answer ........................... and ................................... (2) (Total 6 marks) The Robert Smyth School 6 The Robert Smyth School Mathematics Faculty Y10 Topic 9 Quadratics Innovation & excellence 3. (a) Complete the table of values for y = 2x2 – 4x – 1 x –2 y 15 –1 0 1 –1 2 3 –1 5 (2) (b) 2 On the grid below, draw the graph of y = 2x – 4x – 1 for values of x from – 2 to +3. y (2) 15 14 (c) An approximate solution of the equation 2x2 – 4x – 1 = 0 is x = 2.2 13 12 11 (i) Explain how you can find this from the graph. 10 .............................................................................. 9 .............................................................................. 8 ………………………………………………… 7 ………………………………………………… (1) 6 (ii) Use your graph to write down another solution of this equation. 5 4 Answer x = ............................................... (1) (Total 6 marks) 3 2 1 –2 –1 O 1 2 3 x –1 –2 –3 Success: The Robert Smyth School Target: 7 The Robert Smyth School Mathematics Faculty Y10 Topic 9 Quadratics Innovation & excellence HW3 – Grade A/A* Solving equations using intersecting graphs 1. Teacher Assessment The grid below shows the graph of y = x2 + 3x – 2 y = x 2 + 3x –2 10 9 8 7 6 5 4 3 2 1 –7 –6 –5 –4 –3 –2 –1 O 1 2 3 4 5 6 7 –1 –2 –3 –4 –5 (a) By drawing an appropriate straight line on the graph solve the equation x2 + 3x – 3 = 0 ……….............…............……...................…………….....…………........................ ……….............…............……...................…………….....…………........................ (b) Answer ……………………………….. (2) By drawing an appropriate straight line on the graph solve the equation x2 + 2x – 1 = 0 ……….............…............……...................…………….....…………........................ ……….............…............……...................…………….....…………........................ ……….............…............……...................…………….....…………........................ The Robert Smyth School 8 Answer ………………….…………….. (3) (Total 5 marks) The Robert Smyth School Mathematics Faculty Y10 Topic 9 Quadratics Innovation & excellence 2. The graph of y = x2 – 4x + 8 is shown below. y 14 13 12 11 10 9 8 7 6 5 4 3 2 1 –1 O 1 2 3 4 5 x –1 (a) (i) –2 By drawing the graph of an appropriate straight line, solve the equation x2 – 4x + 8 = 3x – 2 ........................................................................................................................... ........................................................................................................................... Answer .......................................................................... (3) (ii) Hence, or otherwise, solve x2 – 7x + 10 = 0 ........................................................................................................................... ........................................................................................................................... Answer .......................................................................... (1) The Robert Smyth School 9 The Robert Smyth School Mathematics Faculty Y10 Topic 9 Quadratics Innovation & excellence (b) The graph of y = x2 – 4x + 8 is to be used to solve the equation x2 – 5x + 4 = 0 What straight line graph would need to be drawn? (You do not need to draw it, just state its equation.) ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer y = ................................................................... (2) (Total 6 marks) 3. The grid shows the graph of y = x2 + 2x – 5 y 4 2 –4 –3 –2 –1 O 1 x 2 –2 –4 –6 By drawing an appropriate straight line, solve the equation x2 + 2x – 5 = x – 1 ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer ...................................................................... (Total 3 marks) The Robert Smyth School 10 The Robert Smyth School Mathematics Faculty Y10 Topic 9 Quadratics Innovation & excellence 4. (a) Complete the table of values for y = x2 – 2x – 3. –2 x y –1 0 1 2 0 –3 –4 –3 3 4 5 (2) (b) 2 On the grid below, draw the graph y = x – 2x – 3 for values of x between –2 and +4. y (2) 5 (c) Write down the solutions of x2– 2x – 3 = 0 4 ................................................................. Answer ........................................ 3 (1) (d) By drawing an appropriate linear graph, write down the solutions of 2 x2 – x – 4 = 0 ................................................................. 1 …………………………………………. …………………………………………. –2 –1 O 1 2 3 4 x …………………………………………. …………………………………………. –1 …………………………………………. …………………………………………. –2 …………………………………………. –3 Answer.......................................... (3) (Total 8 marks) –4 Success: The Robert Smyth School Target: 11