Quiz 1 Review: Quadratics through 4.2.2
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1 Name: Class: Date: ID: A Quiz 1 Review: Quadratics through Graph each function. How is each graph a translation of f(x) = x 2? 1. y = x y = (x 3) 2 3. y = (x + 3) Which is the graph of y = 2(x 2) 2 4? a. c. b. d. 5. Identify the vertex, axis of symmetry, min/max value, domain and range of the graph of the function y = 2(x + 2) Identify the vertex, axis of symmetry, min/max value, domain and range of the graph of the function y = 2(x + 2)
2 Name: ID: A 7. What steps transform the graph of y = x 2 to y = (x + 3) 2 + 5? 8. Use the vertex form to write the equation of the parabola. 9. Suppose a parabola has vertex ( 8, 7) and also passes through the point ( 7, 4). Write the equation of the parabola in vertex form. 10. Suppose a parabola has an axis of symmetry at x = 8, a maximum height of 1 and also passes through the point (9, 1). Write the equation of the parabola in vertex form. What are the vertex, axis of symmetry, min/max point, domain, and range of the equation? 11. y = 2x x y = 2x 2 + 4x y = 2x 2 + 4x 16 What is the graph of the equation? 14. y = x 2 4x y = x 2 + 2x + 3 What is the vertex form of the equation? 16. y = x 2 2x y = x 2 + 2x 8 2
3 Name: ID: A 18. A ball is thrown into the air with an upward velocity of 28 ft/s. Its height h in feet after t seconds is given by the function h = 16t t + 7. How long does it take the ball to reach its maximum height? What is the ball s maximum height? Round to the nearest hundredth, if necessary. a s; 7 ft b s; ft c s; 17.5 ft d s; ft 19. A catapult launches a boulder with an upward velocity of 148 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h = 16t t How long does it take the boulder to reach its maximum height? What is the boulder s maximum height? Round to the nearest hundredth, if necessary. a s; 30 ft b s; ft c s; ft d s; ft 3
4 Quiz 1 Review: Quadratics through Answer Section 1. ANS: f(x) translated up 2 unit(s) PTS: 1 DIF: L2 REF: 4-1 Quadratic Functions and Transformations TOP: 4-1 Problem 2 Graphing Translations of f(x)=x^2 KEY: graphing quadratic functions translations DOK: DOK 2 2. ANS: f(x) translated to the right 3 unit(s) PTS: 1 DIF: L2 REF: 4-1 Quadratic Functions and Transformations TOP: 4-1 Problem 2 Graphing Translations of f(x)=x^2 KEY: graphing quadratic functions translations DOK: DOK 2 1
5 3. ANS: f(x) translated up 4 unit(s) and translated to the left 3 unit(s). TOP: 4-1 Problem 2 Graphing Translations of f(x)=x^2 KEY: graphing quadratic functions translations DOK: DOK 2 4. ANS: A PTS: 1 DIF: L3 REF: 4-1 Quadratic Functions and Transformations TOP: 4-1 Problem 4 Using Vertex Form KEY: graphing translation DOK: DOK 2 5. ANS: vertex: ( 2, 4); axis of symmetry: x = 2 TOP: 4-1 Problem 3 Interpreting Vertex Form KEY: parabola vertex of a parabola y-intercept DOK: DOK 2 6. ANS: minimum value: 3 domain: all real numbers range: all real numbers 3 TOP: 4-1 Problem 3 Interpreting Vertex Form KEY: parabola vertex of a parabola y-intercept DOK: DOK 2 2
6 7. ANS: reflect across the x-axis, translate 3 units to the left, translate up 5 units TOP: 4-1 Problem 4 Using Vertex Form KEY: parabola vertex of a parabola y-intercept DOK: DOK 2 8. ANS: y = 3(x + 2) PTS: 1 DIF: L2 REF: 4-1 Quadratic Functions and Transformations TOP: 4-1 Problem 5 Writing a Quadratic Function in Vertex Form KEY: parabola equation of a parabola vertex form DOK: DOK 2 9. ANS: y = 3(x + 8) 2 7 TOP: 4-1 Problem 5 Writing a Quadratic Function in Vertex Form KEY: quadratic function equation DOK: DOK ANS: y = 2(x 8) TOP: 4-1 Problem 5 Writing a Quadratic Function in Vertex Form KEY: quadratic function equation DOK: DOK ANS: vertex: ( 5, 31) axis of symmetry: x = 5 PTS: 1 DIF: L2 REF: 4-2 Standard Form of a Quadratic Function STA: A2.1.3 TOP: 4-2 Problem 1 Finding the Features of a Quadratic Function 12. ANS: vertex: ( 1, 1) axis of symmetry: x = 1 PTS: 1 DIF: L3 REF: 4-2 Standard Form of a Quadratic Function STA: A2.1.3 TOP: 4-2 Problem 1 Finding the Features of a Quadratic Function 3
7 13. ANS: minimum value: 9 range: y 9 PTS: 1 DIF: L2 REF: 4-2 Standard Form of a Quadratic Function STA: A2.1.3 TOP: 4-2 Problem 1 Finding the Features of a Quadratic Function 14. ANS: PTS: 1 DIF: L2 REF: 4-2 Standard Form of a Quadratic Function STA: A2.1.3 TOP: 4-2 Problem 2 Graphing a Function of the Form y=ax^2+bx+c 4
8 15. ANS: PTS: 1 DIF: L3 REF: 4-2 Standard Form of a Quadratic Function STA: A2.1.3 TOP: 4-2 Problem 2 Graphing a Function of the Form y=ax^2+bx+c 16. ANS: y = (x 1) PTS: 1 DIF: L2 REF: 4-2 Standard Form of a Quadratic Function STA: A2.1.3 TOP: 4-2 Problem 3 Converting Standard Form to Vertex Form 17. ANS: y = (x 1) 2 7 PTS: 1 DIF: L3 REF: 4-2 Standard Form of a Quadratic Function STA: A2.1.3 TOP: 4-2 Problem 3 Converting Standard Form to Vertex Form 18. ANS: D PTS: 1 DIF: L3 REF: 9-2 Quadratic Functions OBJ: To graph quadratic functions of the form y = ax^2 + bx + c NAT: A.1.e A.2.a A.4.a STA: A3.5.1 A2.1.7 A2.3.1 A2.3.3 A3.3.1 TOP: 9-2 Problem 2 Using the Vertical Motion Model DOK: DOK ANS: D PTS: 1 DIF: L3 REF: 9-2 Quadratic Functions OBJ: To graph quadratic functions of the form y = ax^2 + bx + c NAT: A.1.e A.2.a A.4.a STA: A3.5.1 A2.1.7 A2.3.1 A2.3.3 A3.3.1 TOP: 9-2 Problem 2 Using the Vertical Motion Model DOK: DOK 2 5
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