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## PowerPoint Slideshow about ' Quadratic Functions' - hayley

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Presentation Transcript

Functions

Divison

Inequalities

Functions

Polynomial

Functions &

Graphs

Synthetic

Division

Zeros of

Polynomial

Functions

More on

Polynomial

Zeros

Solving

Inequalities

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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.

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) = 3x2 – 18x + 63. Find the number of automobiles that must be produced to minimize the cost.

Determine if the following is a polynomial function. If so, give the degree.

f(x) = x2 – 3x7

Degree = 7

Use the leading coefficient test to determine the end behavior for

f(x) = 6x3 + 3x2 – 3x - 1

Down to the left.

Find the zeros and their multiplicities of the function.

F(x) = 4(x + 5)(x – 1)2

1, multiplicity 2

f(x) = 4x3 – 6x2 – 5x + 6

Use synthetic division to find all zeros of

f(x) = x3 – 3x2 – 18x + 40.

Use the rational zeros theorem to list all possible rational zeros of f(x) = x5 – 3x2 + 6x + 14

Use the rational zeros theorem to list all possible rational zeros of

f(x) = 3x3 – 17x2 + 18x + 8

and then use this root to find all zeros of the function.

Use Descartes’ Rule of Signs to determine the possible number of positive real zeros and negative real zeros for f(x) = x6 – 8.

1 negative real zero

f(x) = x3 + 5x2 + 12x – 18

Use the Upper Bound Theorem to determine which of the following is a good upper bound for

f(x) = x4 + x3 – 7x2 – 5x + 10

1, 3, 4, or 5

Write the polynomial function as a product of linear factors.

f(x) = x4 – 3x2 – 4

f(x) = x3 + 4x2 – x - 4

Double!!

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

x2 + 3x – 18 > 0

Solve the inequality and give your solution in interval notation.

x2 – 2x – 24 < 0

Solve the inequality and give your solution in interval notation.

x2 – 3x – 10 < 0

Solve the inequality and give your solution in interval notation.

x2 + 6x< – 8

Jeopardy!!

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