# \$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300.

## Presentation on theme: "\$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300."— Presentation transcript:

\$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300 \$400 \$500 \$100 \$200 \$300 \$400 \$500

The graph of the equation is shown below.

What is y = (x + 1) 2 ?

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

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

What is

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

What is f(x) = (x – 3) 2 – 4?

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.

3 thousand automobiles

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

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

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

3x + 8

Divide using synthetic division.

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

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

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

2, 7, 1/3

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

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

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.

-1/3, 2, 4

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

1 positive real zero 1 negative real zero

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

1, -3 + 3i, - 3 – 3i

Use the graphing calculator to determine the zeros of f(x) = x 3 – 6x 2 – 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) = x 4 + x 3 – 7x 2 – 5x + 10 1, 3, 4, or 5

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

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

f(x)= (x – 2)(x + 2)(x – i)(x + i)

Factor completely. f(x) = x 3 + 4x 2 – 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. x 2 + 3x – 18 > 0

(-∞, -6) or (3, ∞)

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

(-4, 6)

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

[-2, 5]

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

[-4, -2]

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

y = (x – 2) 2 (x + 3) 2

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