Graphing Polynomials in Factored Form

Front

What is the y-intercept of f(x)=3x²+4x-5?

Back

-5

Front

The polynomial f(x) = 5x⁴ + 2x³ + 2x - 7 can have, at most, how many solutions?

Back

4

Front

Which of the following could be the equation of this graph in factored form? (Careful-pay attention to multiplicity.)

Back

f(x) = (x+4)(x+1)²(x-2)(x-4)

Front

What effect do odd multiplicities have on the x-axis?

Back

Cross the x-axis

Front

Which is true about the equation of the graph shown?

Back

The function has an Odd degree

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

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

What does the degree of a polynomial indicate?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial and determines the polynomial's end behavior.

Front

What is the significance of the x-intercepts of a polynomial function?

Back

The x-intercepts are the values of x for which the polynomial equals zero, indicating the solutions to the equation.

Front

What is the relationship between the degree of a polynomial and the number of x-intercepts?

Back

A polynomial of degree n can have at most n real x-intercepts.