KEY Algebra: Unit 10 Graphing Quadratic Equations & other Relations

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1 Name: KEY Algebra: Unit 10 Graphing Quadratic Equations & other Relations Date: Test Bank Part I: Answer all 15 questions in this part. Each correct answer will receive credits. No partial credit will be allowed. For each question, write on the separate answer sheet the letter preceding the word or expression that best completes the statement or answers the question. [30] 1. Which ordered pair is a solution to the system of equations y xand [A], [B] 0,0 [C] 1,1 [D], y x?. What are the vertex and the axis of symmetry of the parabola shown in the diagram below? [A] The vertex is, 3 and the axis of symmetry is x = - [B] The vertex is, 3 and the axis of symmetry is y = - [C] The vertex is 3, and the axis of symmetry is y = - [D] The vertex is 3, and the axis of symmetry is x = - 3. Consider the graph of the equation y ax bx c, when a 0. If a is multiplied by 3, what is true of the graph of the resulting parabola? [A] [B] [C] [D] The vertex is 3 units above the vertex of the original parabola. The vertex is 3 units to the right of the original parabola. The new parabola is wider than the original parabola. The new parabola is narrower than the original parabola.

2 4. Which ordered pair is a solution to the system of equations y x1and y x 5x 6? [A] 5, 1 [B] 5, 4 [C] 5,6 [D] 5, 5. A swim team member performs a dive from a 14-foot-high springboard. The parabola below shows the path of her dive. Which equation represents the axis of symmetry? [A] x 3 [B] x 3 [C] y 3 [D] y 3 6. Which equation represents the axis of symmetry of the graph of the parabola below? [A] x 3 [B] x 5 [C] y 3 [D] y 5

3 7. Which ordered pair is a solution to the system of equations y3x15and y x x 0? [A] 5, 30 [B] 0,5 [C] 1, 18 [D] 5, 1 8. What are the vertex and axis of symmetry of the parabola y x 16x 63? [A] Vertex: 8, 17 ; axis of symmetry: x = 8. [B] Vertex: 8,17 ;axis of symmetry: x = 8. [C] Vertex: 8, 17 ; axis of symmetry: x = -8. [D] Vertex: 8,17 ; axis of symmetry: x = The equation y x 3x 18 is graphed on the set of axes below. The roots of a quadratic are where the parabola crosses the x-axis. Based on this graph, what are the roots of the equation x 3x18 0? [A] -3 and 6 [B] 3 and -6 [C] 0 and -18 [D] 3 and The height, y, of a ball tossed into the air can be represented by the equation, y x 10x 3 where x is the elapsed time. What is the equation of the axis of symmetry of this parabola? [A] y 5 [B] x 5 [C] y 5 [D] x 5

4 11. The equation y x x 8is graphed on the set of axes below. Based on this graph, what are the roots of the equation x x8 0? [A] 8 and 0 [B] 9 and -1 [C] and -4 [D] 4 and - 1. Which equation is represented by the graph below? [A] y x 3 [B] y x 3 [C] x 3 y [D] y x 3

5 13. Which ordered pair is a solution to the system of equations shown in the graph below? [A] 1, 3 [B] 0, 1 [C] 1,5 [D] 0, What is the equation of the axis of symmetry of the parabola shown in the graph below? [A] x 0.5 [B] x 4.5 [C] x [D] x 13

6 15. The graph of the equation y x is shown in the diagram below. a must be between -1 and 0. Which diagram could represent a graph of the equation y a x when 1 a 0? [A] [B] [C] [D]

7 16. What are the vertex and the axis of symmetry of the parabola shown in the diagram below? Plug the equation in Y1 and graph. The other roots are the x-intercepts. [A] The vertex is 1, 4 and the axis of symmetry is x = 1 [B] The vertex is 1, 4 and the axis of symmetry is y = -4 [C] The vertex is 4,1 and the axis of symmetry is y = 1 [D] The vertex is 4,1 and the axis of symmetry is x = A student correctly graphed the parabola shown below to solve a given quadratic equation.. Plug the equation in Y1 and graph. The other roots are the x-intercepts. What are the roots of the quadratic equation associated with this graph? [A] -6 and 3 [B] -3 and [C] -6 and 0 [D] - and 3

8 18. Which graph can be used to find the solution of the following system of equations? y x x 3 yx10 [A] [B] [ C] [D] 19. What is the equation of the axis of symmetry of the parabola represented by y x 6x 4? [A] x 3 [B] x 6 [C] y 3 [D] y 6

9 0. The diagram below shows the graph of y x c. Which diagram shows the graph of y x c? [A] [B] [C] [D]

10 1. Which graph represents an exponential equation? [A] [B] [C] [D]. One of the roots of the equation x 3x18 0is 3. What is the other root? [A] 15 [B] -6 [C] 6 [D] What is the solution set of the equation x 5x 0? [A] {0, -5} [B] {0} [C] {0, 5} [D] {5} Plug the equation in Y1 and graph. The other root is the other x-intercept. 4. The solution set of the equation x 4x1 0is [A] {-6, } [B] {-, 6} [C] {-4, 3} [D] {-3, 4

11 5. Which is the graph of y x? [A] [B] [C] [D] Plug the equation into Y1 and graph.

12 6. Which graph could be used to find the solution of the system of equations yx6and y x 4x 3? [A] [B] [C] [D] Plug the equations into Y1 adnd Y and graph them. Match the calculator graph with the choices.

13 Part II: Answer all 3 questions in this part. Each correct answer will receive credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a numerical answer with no work shown will receive only 1 credit. [6] Part III: Answer both questions in this part. Each correct answer will receive 3 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a numerical answer with no work shown will receive only 1 credit. [6] 7. Graph the equation y x x 3on the accompanying set of axes. Using the graph, determine the roots of the equation x x3 0. Roots of a parabola are where it crosses the x-axis. Roots are: x = -1 and x = 3

14 8. On the set of axes below, draw the graph of y x, over the interval 1 x 3. Will this graph ever intersect the x-axis? Justify your answer You only need to graph the x values between -1 and 3. Exponential graphs will NOT cross the x-axis. 9. Find algebraically the equation of the axis of symmetry and the coordinates of the vertex of the parabola whose equation is y x 8x 3. The equation for the axis of b symmetry is: x a 8 8 x x 4 To find the vertex, plug in the x- value from the axis of symmetry b x a y 8 3 y y y 11 (-,11)

15 30. Graph and label the following equations on the set of axes below. y y Explain how decreasing the coefficient of x affects the graph of the equation y x. x 1 x As the coefficient of x decreases, the graph of the absolute value equation gets wider.

16 Part IV: Answer both questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a numerical answer with no work shown will receive only 1 credit. [8] 31. On the set of axes below, solve the following system of equations graphically and state the coordinates of all points in the solution set. y x x 4 5 y x1 The solutions of the system are the coordinates of the intersection points. (-4,-5) and (1, 0)

17 3. On the set of axes below, solve the following system of equations graphically for all values of x and y. y x x 6 1 yx6 The solutions of the system are the coordinates of the intersection points. (-1, 8) and (5, -4)

18 33. On the set of axes below, solve the following system of equations graphically for all values of x and y. y x x 4 1 y x 4 The solutions of the system are the coordinates of the intersection points. (, 0) and (-4, 1)

19 34. Solve the following system of equations algebraically or graphically for x and y. y x x 4 3 y x 1 The solutions of the system are the coordinates of the intersection points. (1, 0) and (4, 3)