Polynomial Graphs - Characteristics

Front

What are the zeros of the polynomial y = 3(x + 4)(x + 1)(x - 3)?

Back

The zeros are -4, -1, and 3.

Front

Which function is graphed? y = -2(x + 3)(x + 1)(x - 2)(x - 5) or y = -\frac{1}{2}(x + 3)(x + 1)(x - 2)(x - 5)?

Back

The function graphed is y = -\frac{1}{2}(x + 3)(x + 1)(x - 2)(x - 5).

Front

What kind of leading coefficient does the function have? f(x) = -2x^2 + 4x - 7

Back

The leading coefficient is negative.

Front

Determine the y-intercept of f(x) = x^3 - 5x^2 - 25x + 7.

Back

The y-intercept is (0, 7).

Front

What is the relative maximum of the function?

Back

The relative maximum is (2, 0).

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 degree of a polynomial?

Back

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

Front

What does the leading coefficient determine in a polynomial function?

Back

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

Front

How do you find the x-intercepts of a polynomial function?

Back

To find the x-intercepts, set the polynomial equal to zero and solve for x.

Front

What is the significance of the y-intercept in a polynomial graph?

Back

The y-intercept is the point where the graph crosses the y-axis, indicating the value of the function when x = 0.