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Published byCatalina Neat Modified over 2 years ago

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The graph of the equation is shown below.

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What is y = (x + 1) 2 ?

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The equation of the parabola with this vertex is f(x) = (x + 8) 2 - 4

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The function for this graph is f(x) = (x – 5) 2 – 1.

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What is

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This quadratic equation has a maximum point at (3, -4).

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What is f(x) = (x – 3) 2 – 4?

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The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x) = 3x 2 – 18x + 63. Find the number of automobiles that must be produced to minimize the cost.

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3 thousand automobiles

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Determine if the following is a polynomial function. If so, give the degree. f(x) = x 2 – 3x 7

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Use the leading coefficient test to determine the end behavior for f(x) = 6x 3 + 3x 2 – 3x - 1

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Up to the right, Down to the left.

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Find the zeros and their multiplicities of the function. F(x) = 4(x + 5)(x – 1) 2

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-1, multiplicity 1 1, multiplicity 2

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Graph the function. F(x) = x 2 (x – 3)(x – 2)

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Use synthetic division to divide. 3x 2 + 29x + 56 x + 7

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3x + 8

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Divide using synthetic division.

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x 4 + 2x 3 + 5x 2 + 10x + 20. R. 45

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Find f(-3) given f(x) = 4x 3 – 6x 2 – 5x + 6

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Solve the equation 3x 3 – 28x 2 + 51x – 14 = 0 given that 2 is one solution.

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2, 7, 1/3

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Use synthetic division to find all zeros of f(x) = x 3 – 3x 2 – 18x + 40.

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Use the rational zeros theorem to list all possible rational zeros of f(x) = x 5 – 3x 2 + 6x + 14

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Use the rational zeros theorem to list all possible rational zeros of f(x) = 3x 3 – 17x 2 + 18x + 8 and then use this root to find all zeros of the function.

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-1/3, 2, 4

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Use Descartes’ Rule of Signs to determine the possible number of positive real zeros and negative real zeros for f(x) = x 6 – 8.

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1 positive real zero 1 negative real zero

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Give all the roots of f(x) = x 3 + 5x 2 + 12x – 18

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1, -3 + 3i, - 3 – 3i

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Use the graphing calculator to determine the zeros of f(x) = x 3 – 6x 2 – x + 6 1, 3, 4, or 5

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1, -1, 6

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Use the Upper Bound Theorem to determine which of the following is a good upper bound for f(x) = x 4 + x 3 – 7x 2 – 5x + 10 1, 3, 4, or 5

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Find all roots of the equation. Hint: -2i is one root. x 4 – 21x 2 – 100 = 0

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Write the polynomial function as a product of linear factors. f(x) = x 4 – 3x 2 – 4

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f(x)= (x – 2)(x + 2)(x – i)(x + i)

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Factor completely. f(x) = x 3 + 4x 2 – x - 4

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f(x)= (x – 1)(x + 1)(x + 4)

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Give an equation for the polynomial function that has zeros of 2, -2, and 3 and has a degree of 3.

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f(x)= (x – 2)(x + 2)(x – 3) Other answers are possible.

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Solve the inequality and give your solution in interval notation. (x – 3)(x + 2) > 0

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(-∞, -2) or (3, ∞)

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Solve the inequality and give your solution in interval notation. x 2 + 3x – 18 > 0

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(-∞, -6) or (3, ∞)

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Solve the inequality and give your solution in interval notation. x 2 – 2x – 24 < 0

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(-4, 6)

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Solve the inequality and give your solution in interval notation. x 2 – 3x – 10 < 0

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[-2, 5]

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Solve the inequality and give your solution in interval notation. x 2 + 6x < – 8

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[-4, -2]

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-10 < x < 10 -10 < y < 60

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y = (x – 2) 2 (x + 3) 2

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Real Zeros of Polynomial Functions. Solve x 3 – 2x + 1 = 0. How? Can you factor this? Can you use the quadratic formula? Now what if I tell you that one.

Real Zeros of Polynomial Functions. Solve x 3 – 2x + 1 = 0. How? Can you factor this? Can you use the quadratic formula? Now what if I tell you that one.

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