Polynomial Graphs

Front

What is the end behavior of the polynomial function f(x) = -5x^4 - 2x^2 + 8?

Back

Left side: Falls, Right side: Falls.

Front

Write a 4th degree polynomial function with a positive leading coefficient and zeros: 9, 3, -2, 0.

Back

y = x(x - 9)(x - 3)(x + 2)

Front

Determine the degree and leading coefficient of the polynomial f(x) = (x-4)^2(x+1).

Back

Odd Degree, + Leading Coefficient.

Front

Select the polynomial whose zeros and degree are given: Zeros: –5 (multiplicity of 3), 9 (multiplicity of 2), –2, 4.

Back

(x + 5)^3(x - 9)^2(x + 2)(x - 4)

Front

Which equation MOST LIKELY matches the graph? y = x^4 - x^3 + 3x^2 + 2, y = -x^4 + x^3 + 5x + 2, y = x^3 - 2x^2 + 1x + 3, y = -x^3 - 2x^2 + 1x + 3.

Back

y = x^4 - x^3 + 3x^2 + 2

Front

What is the definition of a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How do you determine the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is the significance of the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial equals zero; they indicate the x-intercepts of the graph.

Front

What does it mean for a zero to have multiplicity?

Back

Multiplicity refers to the number of times a particular zero is repeated in a polynomial; it affects the shape of the graph at that zero.