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• Slides: 74        \$100 \$200 \$200 \$100 \$200 \$300 \$300 \$400 \$400 \$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) = 3 x 2 – 18 x + 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) = x 2 – 3 x 7    Use the leading coefficient test to determine the end behavior f(x) = 6 x 3 + 3 x 2 – 3 x - 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) = x 2(x – 3)(x – 2)  Use synthetic division to divide. 3 x 2 + 29 x + 56 x+7 3 x + 8 Divide using synthetic division. 4 x + 3 2 x R. 45 + 2 5 x + 10 x + 20. Find f(-3) given f(x) = 4 x 3 – 6 x 2 – 5 x + 6  Solve the equation 3 x 3 – 28 x 2 + 51 x – 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 3 x – 18 x + 40.  Use the rational zeros theorem to list all possible rational zeros of f(x) = x 5 – 3 x 2 + 6 x + 14  Use the rational zeros theorem to list all possible rational zeros of f(x) = 3 3 x – 2 17 x + 18 x + 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 5 x + 12 x – 18  Use the graphing calculator to determine the zeros of f(x) = 3 x – 2 6 x –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 7 x – 5 x + 10  Find all roots of the equation. Hint: -2 i is one root. 4 x – 2 21 x – 100 = 0  Write the polynomial function as a product of linear factors. f(x) = 4 x – 2 3 x – 4  Factor completely. f(x) = 3 x + 2 4 x –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  Solve the inequality and give your solution in interval notation. x 2 + 3 x – 18 > 0  Solve the inequality and give your solution in interval notation. x 2 – 2 x – 24 < 0  Solve the inequality and give your solution in interval notation. x 2 – 3 x – 10 < 0  Solve the inequality and give your solution in interval notation. x 2 + 6 x < – 8     -10 < x < 10 -10 < y < 60 