Math 20 Chapter 5 Review
(Marks are listed to help you understand the value of questions and the amount of work that may be required! You should do all these questions on loose-leaf paper and not on this review.)
A) Quadratic Functions in Vertex Graphing Form (29 marks)
1) Is the following a quadratic function? Why or why not? (1 mark)
y = x(x – 3)
2) What are the values of a, p and q for the function y = -(x – 1)2 + 4? (2 marks)
3) What is the vertex of the function y = -2(x + 2)2 – 1? (2 marks)
4) Graph the quadratic function y = (x – 1)2 – 2. You must state the vertex, include a table of values (use the first 3 staircase numbers), and write out the equation of the axis of symmetry. At the end of this exam you will find a graph page labeled Part A #4.
(5 marks)
5) Graph the quadratic function y = -2(x – 2)2 + 8. You must state the vertex, include a table of values (use the first 3 staircase numbers), and write out the equation of the axis of symmetry. At the end of this exam you will find a graph page labeled Part A #5.
(5 marks)
6) Write the following 3 quadratic functions in order from widest to narrowest. (2 marks)
y = .3x2 + 3 y = 4(x – 1)2 y = -x2
______
7) Given the quadratic function y = 3(x + 2)2 – 2, answer the following questions:
i) Does the graph face Up or Down? Why? (2 marks)
ii) Write the Domain and Range. (2 marks)
iii) Does this function have a minimum or a maximum value? What is the value?
(2 marks)
8) Given the quadratic function y = (x + 2)2 – 25, find the x and y intercepts. (4 marks)
9) Given a quadratic function with a vertex at (-2, 3) and a value of a = -2, how many x-intercepts does this function have? To receive 2 marks, you must include a diagram to explain your answer. (2 marks)
B) Quadratic Functions in Standard Form (14 marks)
Formulas to find vertex (p, q) of a Standard Form Quadratic Function: p = q = c –
1) What are the values of a, b and c for the function y = 2x2 + 4? (2 marks)
2) What is the vertex of the function y = x2 – 6x + 4? (3 marks)
3) Given the quadratic function y = x2 – 3x – 10, find the x and y intercepts. (4 marks)
4) Graph the quadratic function y = x2 – 2x – 4. You must state the vertex, include a table of values (use the first 3 staircase numbers), and write out the equation of the axis of symmetry. At the end of this exam you will find a graph page labeled Part B #4.
(5 marks)
C) Word Problems (12 marks)
1) Below is the graph of the function y = -.003(x – 100)2 + 30 which describes the flight of a golf ball that is hit off the fairway. The distance the ball travels in metres is represented by the variable x. The height of the ball of the ground is represented by the variable y. Based on the graph, answer the following questions:
i) What was the maximum height of the ball? (1 mark)
ii) About how high above the ground was the ball after it traveled 50 metres horizontally?
(1 mark)
iii) Approximately, how far did the ball travel horizontally when the ball was 20 metres above the ground for the second time? (1 mark)
iv) What are the Domain and Range of the above function? (2 marks)
2) Using the equation from question #1 y = -.003(x – 100)2 + 30, calculate the height of the ball to the nearest tenth of a metre after it has traveled 150 metres horizontally. (2 marks)
3) Using the equation from question #1 y = -.003(x – 100)2 + 30, calculate the horizontal distance to the nearest whole metre that the ball traveled down the fairway after it reaches a height of 10 metres for the first time. (2 marks)
4) Find the equation in vertex graphing form y = a(x – p)2 + q of the parabola that is sketched below: (3 marks)
Question: Part A #4
Work Area: Equation is y = (x – 1)2 – 2
(Don’t forget to state the vertex!)
(Show your table of values: use the staircase method!)
(Don’t forget to graph the equation of the axis of symmetry!)
Question: Part A #5
Work Area: Equation is y = -2(x – 2)2 + 8
(Don’t forget to state the vertex!)
(Show your table of values: use the staircase method!)
(Don’t forget to graph the equation of the axis of symmetry!)
Question: Part B #4
Work Area: Equation is y = x2 – 2x – 4
(Don’t forget to state the vertex!)
(Show your table of values: use the staircase method!)
(Don’t forget to graph the equation of the axis of symmetry!)