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Name: _____________________________________________________ Period: ________ Date: ___________________ Group members: ____________________________________________________________________________________ Honors Pre-Calculus 2012-13 Ms. York Chapter 2 Test Review Directions: Below are questions that will help you prepare for the Chapter 2 Test. There will be a calculator part and a noncalculator part for the test. Try to complete the exercises without a calculator where it states “No Graphing Calculator.” Section 2.1 – Quadratic Functions (No Graphing Calculator) 1. Find the vertex, axis of symmetry, x-intercepts, and y-intercepts and then sketch a graph of f (x) 2x 2 12x 16 2. Among all possible inputs for the function g(x) 3x 2 12x 6 which yields the smallest output? What is this minimum output? 3. How far from the origin is the vertex of the parabola y x 2 6x 13 ? 4. Find a quadratic function (in vertex-form) for each problem satisfying the given conditions: a. The graph passes through the origin and the vertex is the center of the circle (x 2) 2 (y 2) 2 16 . b. The axis of symmetry is the line x = 1. The y-intercept is 1. There is only one x-intercept. Section 2.2 – Graphing Polynomials (No Graphing Calculator) 5. What are the characteristics of the graph of a polynomial function? 6. For the following graphs, calculate intercepts, apply leading coefficient test, and use what you know about multiplicity and its effects are on the graphs. a. Graph a sketch of the function y 2(x 3) 4 . 1 b. Graph a sketch of the function f (x) (x 3)(x 1) 3 . 2 7. Give a reason why the following graphs cannot represent a polynomial function of degree 3. Section 2.3 – Polynomial Division (Graphing Calculator Okay) 8. Divide out the following expressions: 2x 2 7x 8 a. x 2 b. 3x 4 2x 3 2 x 2 1 c. x 5 a5 xa 9. When x 3 kx 1 is divided by x 1, the remainder is -4. Find k. Section 2.4 – Complex Numbers (Graphing Calculator Okay) 10. Compute the following (answer should be in standard form a + bi) 5 2i a. 3 4i b. (5 6i) (9 2i) 11. Let z = 2 + 3i, w = 9 – 4i. c. Find zw ___ d. Find z w 12. i101 13. Solve: x 2 4 x 6 0 Section 2.5 – Zeros of polynomials (Graphing Calculator Okay) 14. Find a polynomial equation that satisfies the given conditions. If no such equation is possible, state why. a. Degree 3; three zeros at 3, -4, 5 b. Degree 3; -2 and -3 are zeros c. Degree 3; 4 is a zero of multiplicity two; -1 is a zero of multiplicity two 15. Find all zeros of 2x 4 3x 3 12x 2 22x 60 if given that 1 3i is a zero. Section 2.6 – Rational Functions (No Graphing Calculator) 16. Find domain, intercepts, asymptotes, and critical values, and then sketch a graph for each of the following functions: 3x 15 a. f (x) 4 x 12 b. g(x) (x 2 4)(x 3 1) x6 c. h(x) x2 x 6 x3 d. t(x) x2 9 x3 Section 2.7 – Nonlinear inequalities (Graphing Calculator Okay) 17. Solve the following inequalities (write answers in interval notation) a. x 4 14 x 3 48x 2 b. x3 0 x4 c. 2x 1 2 1 x 1 x 3