AAC #5 Graphing Polynomials

Front

What are the roots of the polynomial f(x) = (x+1)(x-4)(x+2)?

Back

The roots are -1, 4, and -2.

Front

How do you identify the relative minimum of a polynomial function?

Back

The relative minimum can be found by analyzing the graph or using calculus to find critical points.

Front

What is the end behavior of the polynomial f(x) = -2x^2 + 3x?

Back

The end behavior is Left down and Right down.

Front

What determines the end behavior of a polynomial function?

Back

The degree and the sign of the leading coefficient determine the end behavior.

Front

What is the degree and leading coefficient of the polynomial f(x) = 2x^3 - x + 5?

Back

The degree is 3 (odd) and the leading coefficient is positive.

Front

What is 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 the polynomial.

Front

How do you find the roots of a polynomial?

Back

You can find the roots by factoring the polynomial, using the quadratic formula, or graphing.

Front

What does it mean for a polynomial to have a relative maximum?

Back

A relative maximum is a point where the polynomial reaches a peak compared to nearby points.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable and affects the shape and number of roots.