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Exam 2: Polynomial and Rational Functions

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Question 51

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For the given graph: (a) list each real zero and its smallest possible multiplicity; (b) determine whether the degree of the polynomial is even or odd; (c) determine whether the leading coefficient of the polynomial is positive or negative; (d) find the y-intercept; (e) write an equation for the polynomial function (assume the least degree possible).

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Question 52

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Find the standard form of the equation of a parabola whose vertex is and passes through the point

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Question 53

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Factor the polynomial as a product of linear factors.

For the polynomial function , find the y - intercept.

Rewrite the quadratic equation in standard form by completing the square. Y = x² - 9x

Find a polynomial of minimum degree that has these zeros. 0, 3 + 3i, 3 - 3i

Match the polynomial function with its graph.

Use long division to divide 9x³ + 36x² + 57x + 42 by 3x + 6.

Divide the polynomials using synthetic division.

For the rational function , find the equation of the slant asymptote.

Find a polynomial of minimum degree that has the zeros (with multiplicity 2) and (with multiplicity 2) .

Use Descarte's Rule of signs to determine the possible number of positive real zeros and negative real zeros. P(x) = 5x³ + 2x² + 4x - 9

Rewrite the quadratic function in standard form by completing the square.

Use the intermediate value theorem to approximate the real zero in the indicated interval. Approximate to two decimal places.

Divide the polynomials by either long division or synthetic division.

A rancher has 600 linear feet of fencing and wants to enclose a rectangular field and then divide it into two equal pastures with an internal fence parallel to one of the rectangular sides. What is the maximum area of each pasture?

Find the vertex of the parabola associated with the quadratic function.

Sketch the graph of the polynomial function, , using transformations of known polynomial functions.

Use the rational zero theorem to list the possible rational zeros. P(x) = 7x³ - 4x² + 3x - 21

Find the equation for the graph.