1. Graph the quadratic function ƒ1x2 = -2x2 + 6x - 3. Give the intercepts, vertex, axis, domain, range, and the largest open intervals of the domain over which the function is increasing or decreasing. 2. (Modeling) Height of a Projectile A small rocket is fired directly upward, and its height s in feet after t seconds is given by the function s1t2 = -16t2 + 88t + 48. (a) Determine the time at which the rocket reaches its maximum height. (b) Determine the maximum height. (c) Between what two times (in seconds, to the nearest tenth) will the rocket be more than 100 ft above ground level? (d) After how many seconds will the rocket hit the ground? Use synthetic division to perform each division. 3. 3x3 + 4x2 - 9x + 6 x + 2 4. 2x3 - 11x2 + 25 x - 5 5. Use synthetic division to determine ƒ152 for ƒ1x2 = 2x3 - 9x2 + 4x + 8. 6. Use the factor theorem to determine whether the polynomial x - 3 is a factor of 6x4 - 11x3 - 35x2 + 34x + 24. If it is, what is the other factor? If it is not, explain why. 7. Given that -2 is a zero, find all zeros of ƒ1x2 = x3 + 8x2 + 25x + 26. 8. Find a fourth-degree polynomial function ƒ having only real coefficients, -1, 2, and i as zeros, and ƒ132 = 80. 9. Consider the polynomial function ƒ1x2 = x3 - 5x2 + 2x + 7. (a) Use the intermediate value theorem to show that ƒ has a zero between 1 and 2. (b) Use Descartes’ rule of signs to determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros. (c) Use a graphing calculator to find all real zeros to as many decimal places as the calculator will give. 10. Graph the following polynomial functions on the same axes. ƒ1x2 = x4 and g1x2 = -21x + 524 + 3 How can the graph of g be obtained by a transformation of the graph of ƒ? Chapter 3 Test 431 CHAPTER 3 Test 93. Power of a Windmill The power a windmill obtains from the wind varies directly as the cube of the wind velocity. If a wind of 10 km per hr produces 10,000 units of power, how much power is produced by a wind of 15 km per hr? 94. Pressure in a Liquid The pressure on a point in a liquid is directly proportional to the distance from the surface to the point. In a certain liquid, the pressure at a depth of 4 m is 60 kg per m2. Find the pressure at a depth of 10 m.
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