WorkSHEET 9.1 Quadratic graphs Name: ___________________________ © John Wiley & Sons Australia, Ltd Page 16 1 Plot the graph of y = x2 for values of x from −3 to 3 inclusive. State the equation of the axis of symmetry and the coordinates of the turning point. 2 Plot the graph of y = −x2 for values of x from −3 to 3 inclusive. State the equation of the axis of symmetry and the coordinates of the turning point. © John Wiley & Sons Australia, Ltd Page 17 3 Plot the graph of y = x2 – 1 for values of x from −3 to 3 inclusive. State the equation of the axis of symmetry and the coordinates of the turning point. 4 Plot the graph of y = (x – 1)2 for values of x from −3 to 3 inclusive. State the equation of the axis of symmetry and the coordinates of the turning point. © John Wiley & Sons Australia, Ltd Page 18 5 Plot the graph of y = (x + 1)2 1 for values of x from −3 to 3 inclusive. State the equation of the axis of symmetry and the coordinates of the turning point. 6 For the equation y = x2 + 2: (a) state the vertical translation (b) state the coordinates of the turning point (c) sketch the curve. © John Wiley & Sons Australia, Ltd Page 19 7 For the equation y = (x + 2)2: (a) state the horizontal translation (b) state the coordinates of the turning point (c) sketch the curve. 8 Sketch the graph of the following quadratic equations: (a) y = 2x2 (b) y= 1 2 x 2 © John Wiley & Sons Australia, Ltd Page 20 9 On the same set of axes, sketch the graphs of the quadratic equations y = x2 and y = −x2. 10 Sketch each of the following quadratic equations: (a) y = −(x – 2)2 (b) y = 2 – x2 © John Wiley & Sons Australia, Ltd Page 21 1 For each of the following graphs, state the coordinates of the turning point and whether it is a maximum or a minimum: (a) y = (x + 3)2 7 (b) 2 For each of the following graphs, state the coordinates of the turning point, whether it is a maximum or a minimum, and whether it is narrower or wider than y = x2. (a) y = 0.2(x – 5)2 4 (b) 3 y = −(x – 4)2 + 2 y = −6(x + 4)2 + 9 Describe the translations required to change y = x2 into: (a) y = (x – 7)2 + 6 (b) y = (x + 8)2 – 9 © John Wiley & Sons Australia, Ltd Page 23 4 State the equation of each of the following: (a) (b) 5 For the equation y = (x – 2)2 + 5: (a) state the coordinates of the turning point (b) state whether it is a maximum or minimum (c) state the y-intercept (d) state if it is wider or narrower than y = x2 (e) sketch the curve. © John Wiley & Sons Australia, Ltd Page 24 6 7 For the equation y = −(x + 1)2 – 4: (a) state the coordinates of the turning point (b) state whether it is a maximum or minimum (c) state the y-intercept (d) state if it is wider or narrower than y = x2 (e) sketch the curve. For the equation y = 2(x 1)2 – 3: (a) state the coordinates of the turning point (b) state whether it is a maximum or minimum (c) state the y-intercept (d) state if it is wider or narrower than y = x2 (e) sketch the curve. © John Wiley & Sons Australia, Ltd Page 25 8 Complete the square on each of the following to find the equation, and therefore the coordinates of the turning point: (a ) y 2 x 2 10 x 9 (b) y 3x 2 11x 1 © John Wiley & Sons Australia, Ltd Page 26 9 Sketch the graph of y = x2 + 4x + 9 using the completing the square method to find the coordinates of the turning point. 10 Sketch the graph of y x 2 6 x 7 using the x-intercepts to find the coordinates of the turning point. © John Wiley & Sons Australia, Ltd Page 27