RF Unit Test # Review Quadratics (Chapter 6) 1. What is the degree of a quadratic function? Name: a. 1 b. c. 3 d. 0. What is the -intercept for = 3x + x 5? a. 5 b. 5 c. d. 3 3. Which set of data is correct for this graph? 3 1 5 3 1 1 3 5 x 1 3 5 a. Set A. b. Set B. c. Set D. d. Set C. Set Axis of Smmetr Vertex Domain Range A. x = (, 6) x R R B. x = (, ) 8 x 8 C. x = (, ) x R D. x = (, 6) x 7. What are the x- and -intercepts for the function f(x) = x + 5x + 6? a. x = -, x= -, = 6 b. no x-intercepts, = 6 c. x = -.5, = 6 d. x= -3, x= -, = 6 5. The points (, ) and (1, ) are located on the same parabola. What is the equation for the axis of smmetr for this parabola? a. x = 0.5 b. x = 1 c. x = 0.5 d. x = 1.5 6. Find the zero s of: x 5x = a. x =, x = 1 b. x =, x = 1 c. x =, x = 1 d. x =, x = 1 7. What is the correct quadratic function for this parabola? 8. What is the correct quadratic function for this parabola? 3 5 1 5 3 1 1 3 5 x 1 3 5 7 a. f(x) = (x )(x 3) b. f(x) = (x + )(x 3) c. f(x) = (x )(x + 3) d. f(x) = (x + )(x + 3) 3 1 5 3 1 1 3 5 x 1 3 5 a. f(x) = (x 1)(x + 3) b. f(x) = (x + 1)(x + 3) c. f(x) = (x + 1)(x 3) d. f(x) = (1 x)(3 x)
9. Which set of data is correct for the quadratic relation f(x) = (x 0.5)(x + 1)? 10. Which relation is the factored form of f(x) = x + x 3? a. f(x) = x(x + ) + 3 b. f(x) = (x ) c. f(x) = (x + 3)(x 1) d. f(x) = (x 3)(x + 1) 11. Which relation is the factored form of f(x) = 3x 3x + 6? a. f(x) = 3(x + )(1 x) b. f(x) = 3(x + )(x 1) c. f(x) = (3x 3) d. f(x) = 3(x + 3) 1. Solve 5x 36 = 0 b factoring. 13. Solve 3 + 1 = 0 using the quadratic formula. a. = 1, = b. = 1, = c. = 1, = d. = 1, = 1. Which parabola opens upward? a. = x x 5 b. = + x 5x c. = x 5x d. = 5x + x + a. x =, x = b. x =, x = 5 c. x = 6, x = d. x =, x = 16. Which set of data is correct for this graph? 1 1 10 8 15. What are the x- and -intercepts for the function f(x) =x x + 3? a. no x-intercepts, = 3 b. x = 0, x = 3, = c. x = 1, x = 3, = 3 d. x = 3, x = 1, = 3 Axis of Smmetr Vertex Domain Range A. x = 3 (3, ) x R B. x = 3 (, 3) x R R C. x = (, 3) 1 x 7 D. x = 3 (3, ) x 8 0 6 3 1 1 3 5 6 7 x a. Set A. b. Set C. c. Set D. d. Set B. Short Answer 17. If a parabola with equation = ax + bx + c opens downward, will a be positive or negative? 18. If a parabola with equation = ax + bx + c has a -intercept above the x-axis, will c be positive or negative?
19. Fill in the table for the relation = -x + 1x + 1. -intercept x-intercept(s) Axis of smmetr Vertex Domain Range 0. Make a table of values, then sketch the graph of the relation = x x + 7. 1. Fill in the table for the relation = x 6x. USE GRAPHING CALCULATOR! Maximum or minimum Axis of smmetr Vertex. Solve x 8x + 15 = 0 b graphing the corresponding function and determining the zeros (without a graphing calculator). 3. Determine the roots of the corresponding quadratic equation for the graph.. A quadratic function has an equation that can be written in the form f(x) = a(x r)(x s). The graph of the function has x-intercepts at (3, 0) and (6, 0) and passes through the point (7, ). Write the equation of the function. 5. Fill in the table for the quadratic function f(x) = (x )(x 6). -intercept Zeros Axis of smmetr Vertex 6. Sketch the graph of the relation = (x )(x 6), then state the domain and range. 7. Determine the equation that defines a quadratic function with x-intercepts located at (, 0) and (1, 0) and a -intercept of (0, ). Provide a sketch to support our work. 8. Solve x + 15x + 9 = 0 b factoring. 9.Solve x + 3x = x 1 using the quadratic formula. Verif our solution
Problems 30. A skier s jump can be modelled b the function =.9x + 3.x +.5, where is the skier's height above the ground, in metres, and x is the time, in seconds, that the skier is in the air. a) Use technolog to sketch graph the function from our graphing calculator. b) Determine the coordinates of the vertex. c) Determine the skier s maximum height in metres. d) Determine the domain and range of this function. 31. Determine the equation for this quadratic function. Write the equation in standard form. Show all our steps. 0 35 30 5 0 15 10 5 8 7 5 3 1 1 x 5 10 3. 33. Use the discriminant to determine the number of roots: a) = x x 1 b) = x + x + 100
RF Unit Test Review Answer Section MULTIPLE CHOICE 1. ANS: B. ANS: A 3. ANS: D. ANS: D 5. ANS: A 6. ANS: D 7. ANS: C 8. ANS: C 9. ANS: B 10. ANS: C 11. ANS: B 1. ANS: A 13. ANS: D 1. ANS: D 15. ANS: A 16. ANS: A SHORT ANSWER 17. ANS: negative 18. ANS: positive 19. ANS: -intercept (0, 1) x-intercept(s) & -3 Axis of smmetr x = 0.5 Vertex (0.5, 10.5) Domain x R Range 10.5 0. ANS: x 13 1 9 0 7 1 7 9 3 13 16 1 1 10 8 6 5 3 1 1 3 5 x
1. ANS: Maximum or minimum minimum Axis of smmetr x = 3 Vertex (3, 13). ANS: x = 5, x = 3 3. ANS: There are no roots.. ANS: f(x) = (x 3)(x 6) 5. ANS: -intercept = Zeros (, 0), (6, 0) Axis of smmetr x = 5 Vertex (5, 1) 6. ANS: x R, 1 7 6 5 3 1 1 1 3 5 6 7 8 9 x 1 3 7. ANS: = 0.5(x )(x 1) 8 6 6 8 10 1 1 x 8 10 1
8. ANS:, x = 3 9. ANS: x =, x = 3 30. ANS: a) b) (0.33, 3.0) c) The skier s maximum height is 3.0 m. d) Domain: 0 x 1.1 Range: 0 3.0 31. ANS: The x-intercepts are ( 5, 0) and (, 0), so r = 5 and s =. The graph opens upward so a > 0. = a(x r)(x s) = a[x ( 5)](x ( )) = a(x + 5)(x + ) The -intercept is (0, 0). = a(x + 5)(x + ) 0 = a(0 + 5)(0 + ) 0 = 10a = a So, = (x + 5)(x + ) In standard form: = (x + 5)(x + ) = (x + 5x + x + 10) = x + 1x + 0
3. 33. Use the discriminant to determine the number of roots: a) = x x 1 b) = x + x + 100 b ac b ac (-) ()(-1) () (1)(100) 16 (-8) 16 00 + ( roots) -38 (no roots)