Quadratics Unit Review

Transcription

1 Name: Class: Date: Quadratics Unit Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. (2 points) Consider the graph of the equation y = ax 2 + bx + c, when a 0. If a is multiplied by 1, what is true 3 of the graph of the resulting parabola? a. The vertex is 3 units above the vertex of the original parabola. b. The new parabola is 3 units to the right of the original parabola. c. The new parabola is wider than the original parabola. d. The new parabola is narrower than the original parabola. 2. (2 points) 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 c. x = 23 b. y = 3 d. y = (2 points) What are the vertex and axis of symmetry of the parabola y = x 2 16x + 63? a. vertex: (8, 1); axis of symmetry: x = 8 b. vertex: (8,1); axis of symmetry: x = 8 c. vertex: ( 8, 1); axis of symmetry: x = 8 d. vertex: ( 8,1); axis of symmetry: x = 8 1

2 Name: 4. (2 points) The equation y = x 2 + 3x 18 is graphed on the set of axes below. Based on this graph, what are the roots of the equation x 2 + 3x 18 = 0? a. 3 and 6 c. 3 and 6 b. 0 and 18 d. 3 and (2 points) What are the roots of the equation ( x 6) ( x 1) = 0? a. 1 and 7 c. 1 and 6 b. 1 and 7 d. 1 and 6 6. (2 points) What is the solution set of the equation x 2 10x + 21 = 0? a. {1, 21} c. {3, 7} b. {-5, -5} d. {-3, -7} 7. (2 points) The solution set for the equation r 2 4r = 12 is a. {3, 2} c. {3, 0} b. {6, 2} d. {6, 3} 8. (2 points) Which ordered pair is a solution of the system of equations y = x 2 x 20 and y = 3x 15? a. ( 5, 30) c. (0,5) b. ( 1, 18) d. (5, 1) 2

3 Name: 9. (2 points) The length of a rectangular room is 7 less than two times the width, w, of the room. Which expression represents the area of the room? a. 2w 5 c. 2w 2 5w b. 2w 7 d. 2w 2 7w 10. (2 points) The accompanying diagram shows the graphs of a linear equation and a quadratic equation. How many solutions are there to this system of equations? a. 1 c. 3 b. 2 d (2 points) The value of the expression a b when a = 7 and b = 3 is a. 10 c. 4 b. 10 d (2 points) Multiply. (6w + 6z ) 2 a. 36w w z + 36z 2 c. 36w w z + 36z 2 b. 36w z 2 d. 12w z 2 3

4 Name: 13. (2 points) Which graph represents a function? a. c. b. d. Short Answer 14. (3 points) Find algebraically the equation of the axis of symmetry and the coordinates of the vertex of the parabola whose equation is y = 2x 2 + 8x 1. Equation for axis of symmetry: Coordinates of vertex: _ 4

5 Name: 15. (4 points) 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 2 + 4x 5 y = x (4 points) BONUS: A rectangle has an area of 24 square units. The width is 5 units less than the length. What is the length, in units, of the rectangle? (Hint: algebraic solution requires solving a quadratic!) 5

6 Quadratics Unit Review Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 2 REF: ia STA: A.G.5 TOP: Graphing Quadratics 2. ANS: A PTS: 2 REF: ia STA: A.G.10 TOP: Identifying the Vertex of a Quadratic Given Graph 3. ANS: A PTS: 2 REF: ia STA: A.A.41 TOP: Identifying the Vertex of a Quadratic Given Equation 4. ANS: C PTS: 2 REF: ia STA: A.G.8 TOP: Solving Quadratics by Graphing 5. ANS: D PTS: 2 REF: ia STA: A.A.28 TOP: Roots of Quadratics 6. ANS: C PTS: 2 REF: ia STA: A.A.28 TOP: Solving Quadratics by Factoring 7. ANS: B r 2 4r = 12 The equation is in the form ar 2 + br = c. r 2 4r + 4 = Ê b Add 2 Ë Á ˆ 2 to both sides of the equation. ( r 2) = 16 Factor the perfect square trinomial. r 2 = ±4 Take the square root of both sides of the equation. r = ±4 + 2 Solve. r = 6 or r = 2 The solutions are 6 and 2. A B C D Feedback Add (b/2)^2 to both sides of the equation and factor the perfect square trinomial. Correct! Add (b/2)^2 to both sides of the equation and factor the perfect square trinomial. Add (b/2)^2 to both sides of the equation and factor the perfect square trinomial. PTS: 2 DIF: Average REF: Page 646 OBJ: Solving x^2+bx=c by Completing the Square NAT: a STA: A.A.8 TOP: 9-8 Completing the Square 8. ANS: B PTS: 2 REF: ia STA: A.A.11 TOP: Quadratic-Linear Systems 9. ANS: D PTS: 2 REF: ia STA: A.A.1 TOP: Geometric Applications of Quadratics 10. ANS: B PTS: 2 REF: a STA: A.G.9 TOP: Quadratic-Linear Systems 11. ANS: A PTS: 2 REF: ia STA: A.N.6 TOP: Absolute Value 1

7 12. ANS: C Method 1 ( a + b) 2 = a 2 + 2ab + b 2 The factors fit the pattern for squaring a binomial to get a perfect square trinomial. Use the rule for ( a + b) 2. a = 6w and b = 6z a 2 = 36w 2 2ab = 72wz b 2 = 36z 2 ( a + b) 2 = a 2 + 2ab + b 2 Identify a and b from the given binomial. Use these values to determine a 2, 2ab, and b 2. Substitute the terms into the corresponding places. (6w + 6z ) 2 = 36w w z + 36z 2 Method 2 (6w + 6z ) 2 = (6w + 6z )(6w + 6z ) Use FOIL to multiply the binomials. = 36w w z + 36w z + 36z 2 = 36w w z + 36z 2 A B C D Feedback Check your multiplication and addition. Rewrite the binomial square as a product of two binomials. Either use FOIL or the rule for squaring a binomial. Correct! Rewrite the binomial square as a product of two binomials. Either use FOIL or the rule for squaring a binomial. PTS: 2 DIF: Average REF: Page 501 OBJ: Finding Products in the Form (a + b)^2 NAT: c STA: A.A.13 TOP: 7-8 Special Products of Binomials 13. ANS: D PTS: 2 REF: ia STA: A.G.3 TOP: Defining Functions SHORT ANSWER 14. ANS: x = 2; (2,7) PTS: 3 REF: ia STA: A.A.41 TOP: Identifying the Vertex of a Quadratic Given Equation 2

8 15. ANS: PTS: 4 REF: ia STA: A.G.9 TOP: Quadratic-Linear Systems 16. ANS: 8 PTS: 4 REF: ia STA: A.A.8 TOP: Geometric Applications of Quadratics 3