Graphing Polynomials

Front

What is the y-intercept of the polynomial function f(x) = x^3 - 5x^2 - 25x + 125?

Back

The y-intercept is (0, 125).

Front

How many zeros does the polynomial function P(x) = 3x^4 + 4x - 8 have?

Back

The polynomial has 4 zeros.

Front

Identify the zeros of the polynomial function that has the solutions x = -2, x = 0, x = 1.

Back

The zeros are x = -2, x = 0, x = 1.

Front

What is the maximum number of solutions for the polynomial f(x) = 5x^4 + 2x^3 + 2x - 7?

Back

The maximum number of solutions is 4.

Front

Define 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 degree of a polynomial?

Back

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

Front

What does it mean for a polynomial to have a zero at x = a?

Back

It means that when x = a, the polynomial evaluates to zero, i.e., P(a) = 0.

Front

How can you find the y-intercept of a polynomial function?

Back

To find the y-intercept, evaluate the polynomial at x = 0.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have at most n zeros.