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$100 $100 $100 $100 $200 $200 $200 $200 $300 $300 $300 $100 $100 $200 $200 $300 $300 $300 $400 $400 $400 $400 $400 $400 $500 $500 $500 $500 $500 $500 The graph of the equation is shown below. What is y = (x + 2 1) ? The equation of the parabola with this vertex is f(x) = (x + 8)2 - 4 The function for this graph is f(x) = (x – 2 5) – 1. What is This quadratic equation has a maximum point at (3, -4). What is f(x) = (x – 2 3) – 4? The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x) = 3x2 – 18x + 63. Find the number of automobiles that must be produced to minimize the cost. 3 thousand automobiles Determine if the following is a polynomial function. If so, give the degree. f(x) = x2 – 3x7 Use the leading coefficient test to determine the end behavior for f(x) = 6x3 + 3x2 – 3x - 1 Up to the right, Down to the left. Find the zeros and their multiplicities of the function. F(x) = 4(x + 5)(x – 1)2 -1, multiplicity 1 1, multiplicity 2 Graph the function. F(x) = x2(x – 3)(x – 2) Use synthetic division to divide. 3x2 + 29x + 56 x+7 3x + 8 Divide using synthetic division. x x 5 x2 5 3 4 x + 3 2x R. 45 + 2 5x + 10x + 20. Find f(-3) given f(x) = 4x3 – 6x2 – 5x + 6 Solve the equation 3x3 – 28x2 + 51x – 14 = 0 given that 2 is one solution. 2, 7, 1/3 Use synthetic division to find all zeros of f(x) = 3 x – 2 3x – 18x + 40. Use the rational zeros theorem to list all possible rational zeros of f(x) = x5 – 3x2 + 6x + 14 1, 2, 7, 14 Use the rational zeros theorem to list all possible rational zeros of f(x) = 3 3x – 2 17x + 18x + 8 and then use this root to find all zeros of the function. -1/3, 2, 4 Use Descartes’ Rule of Signs to determine the possible number of positive real zeros and negative real 6 zeros for f(x) = x – 8. 1 positive real zero 1 negative real zero Give all the roots of f(x) = 3 x + 2 5x + 12x – 18 1, -3 + 3i, - 3 – 3i Use the graphing calculator to determine the zeros of f(x) = 3 x – 2 6x –x+6 1, 3, 4, or 5 1, -1, 6 Use the Upper Bound Theorem to determine which of the following is a good upper bound for f(x) = 4 x + 3 x – 1, 3, 4, or 5 2 7x – 5x + 10 Find all roots of the equation. Hint: -2i is one root. x4 – 21x2 – 100 = 0 Write the polynomial function as a product of linear factors. f(x) = 4 x – 2 3x –4 f(x)= (x – 2)(x + 2)(x – i)(x + i) Factor completely. f(x) = 3 x + 2 4x –x-4 f(x)= (x – 1)(x + 1)(x + 4) Give an equation for the polynomial function that has zeros of 2, -2, and 3 and has a degree of 3. f(x)= (x – 2)(x + 2)(x – 3) Other answers are possible. Solve the inequality and give your solution in interval notation. (x – 3)(x + 2) > 0 (-∞, -2) or (3, ∞) Solve the inequality and give your solution in interval notation. x2 + 3x – 18 > 0 (-∞, -6) or (3, ∞) Solve the inequality and give your solution in interval notation. x2 – 2x – 24 < 0 (-4, 6) Solve the inequality and give your solution in interval notation. x2 – 3x – 10 < 0 [-2, 5] Solve the inequality and give your solution in interval notation. x2 + 6x < – 8 [-4, -2] -10 < x < 10 -10 < y < 60 y = (x – 2)2(x + 3)2