Graphing Polynomials Flashcardziz Game

Front

What are the zeros of the function f(x)=(x+4)(x-3)(x-2)?

Back

The zeros are x=-4, x=3, x=2.

Front

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

Back

The multiplicity of that zero is odd.

Front

Describe the end behavior of a polynomial function where the leading coefficient is positive and the degree is odd.

Back

As x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞.

Front

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

Back

The leading coefficient is 2.

Front

How do you find the zeros of a polynomial function?

Back

Set the function equal to zero and solve for x.

Front

What does it mean if a polynomial has a zero with even multiplicity?

Back

The graph touches the x-axis at that zero but does not cross it.

Front

What is the degree of the polynomial f(x) = 4x^5 - 3x^3 + 2?

Back

The degree is 5.

Front

How can you determine the number of possible real zeros of a polynomial?

Back

The number of possible real zeros is at most equal to the degree of the polynomial.

Front

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

Back

The y-intercept is the value of the function when x=0.

Front

What is the relationship between the degree of a polynomial and its end behavior?

Back

The end behavior is determined by the leading term; even degree means both ends go in the same direction, odd degree means they go in opposite directions.