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Name: Date: Algebra 2 Quadratic Functions: Review 1. Write f(x) formulas for quadratic functions that have the specified zeros. (For most of the functions, it might be easiest to write a factored form first.) Then, convert the formulas into standard (ax2 + bx + c) form. a. with zeros 3 and –2 b. with zeros –4 and 2 3 c. with zeros –2.5 and 0 d. with 5 as the only zero e. with no zeros Hint: Can’t start from factored form for this one. Name: Date: Algebra 2 2. Find the (x, y) coordinates of the vertex of these functions, using the specified methods. a. f(x) = x2 – 8x – 4, by putting the function into vertex form using completing the square. b. f(x) = –2x2 + 12x – 10, by factoring to find the zeros, then using the zeros c. f(x) = 2x2 – 7x + 13, using the formula that contains a and b Name: Date: 2. (continued) Find the (x, y) coordinates of the vertex of these functions… d. h(t) = –16t2 + 50t + 10, graphically on the calculator e. f(x) = –3x2 – 12x + 8, by putting the function into vertex form f. f(x) = –4(x + 3)2 + 5, using the easiest method available g. f(x) = 2(x – 3)(x – 7), using the easiest method available h. f(x) = 42x2 – 10x + 19, using your choice of method Algebra 2 Name: Date: 3. Do all of the following for the function f(x) = –2x2 + 4x + 6. a. Using factoring, find the zeros. b. Using completing-the-square, find the vertex. c. Find the y-intercept. d. Draw the 4 points found so far, then sketch the graph of f(x). Algebra 2 Name: Date: 4. Answer these questions for the function f(x) = –3(x + 2)2 + 9. a. What are the coordinates of the vertex? b. What is the equation for the axis of symmetry? c. Find the y-intercept. d. Using an algebraic (non-graphical) method, find the zeros. e. Sketch a graph of f(x) using the information found above. Algebra 2 Name: Date: Algebra 2 5. Solve these equations algebraically (not graphically). If a method is stated, you must use that method. Show your solving steps. a. 10 x 2 33x 7 . Solve by factoring. b. 2 x 2 12 x 18 . Solve by completing the square. c. 6x2x 1 0 d. 2x 12 5 1 Name: Date: 6. Find a quadratic function formula for each set of information given below. a. The zeroes of the function are -3 and 6, and f(3) = 6 b. The minimum point of the parabola is (-2, 4) and f(0) = 12 Algebra 2 Name: Date: Algebra 2 Answers to “Quadratic Functions: Review” 1. a. f(x) = (x – 3)(x + 2) = x2 – x – 6. b. f(x) = (x + 4)(x – 2 3 ) = x2 + 10 3 x– 8 3 or f(x) = (x + 4)(3x – 2) = x2 + 10x – 8. c. f(x) = (x + 2.5)(x – 0) = x2 + 2.5x. d. f(x) = (x – 5)2 = x2 – 10x + 25. e. There are many correct answers. Pick one of these strategies: o Write f(x) = ax2 + bx + c picking any numbers a, b, and c that make b2 – 4ac negative. o Write f(x) = a(x – h)2 + k picking (h, k) to be any point above the x-axis, and a > 0. o Use the fact that x2 is never negative to write a formula that can’t possibly equal 0, such as f(x) = x2 + 1. 2. a. f(x) = (x – 4)2 – 20; vertex (4, –20). b. Zeros are 1 and 5, whose average is 3; vertex (3, 8). c. x = - b 2a = 7 4 ; vertex (1.75, 6.875). d. Vertex ≈ (1.56, 49.06). e. f(x) = –3(x + 2)2 + 20; vertex (–2, 20). f. It’s in vertex form, so vertex (–3, 5). g. Easiest to average the zeros; vertex (5, –8). h. Graphically on the calculator is probably easiest; vertex (0.12, 18.40). 3. a. f(x) = (–2x + 6)(x + 1); zeros 3 and –1. b. f(x) = –2(x – 1)2 + 8; vertex (1, 8). c. f(0) = 6. d. See graph at right. Name: Date: Algebra 2 4. a. (–2, 9) b. x = –2 c. f(0) = –3. d. x = -2 ± 3 e. Graph shown at the right, includes points (–2, 9), (–3.73, 0), (–0.27, 0), and (0, –3). 5. a. 2 x 75 x 1 0, therefor e x 7 1 ,x 2 5 b. x 3 18 3 3 2 (second form is not required) c. x = 0, x = ½ d. x 1 2 (Taking square roots is easiest method.) 6. a. b. 1 f (x) = - (x + 3)(x - 6) 3 f (x) = 2(x + 2)2 + 4