5.2.6 Review B Flashcard Review

Front

What is the general shape of the graph of a polynomial function with an even degree and a negative leading coefficient?

Back

The graph falls to the right and rises to the left.

Front

What does it mean for a polynomial function to have a relative minimum?

Back

A relative minimum is a point on the graph where the function value is lower than all nearby points.

Front

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

Back

Set the polynomial equal to zero and solve for x.

Front

What is the significance of the multiplicity of a root in a polynomial function?

Back

The multiplicity indicates how the graph behaves at the x-intercept: odd multiplicity means it crosses the x-axis, while even multiplicity means it bounces off.

Front

What is the absolute maximum of a function?

Back

The absolute maximum is the highest point over the entire domain of the function.

Front

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

Back

Substitute x = 0 into the polynomial and solve for y.

Front

What is the range of a polynomial function with a leading coefficient that is negative?

Back

The range is typically from negative infinity to the maximum value of the function.

Front

What does the term 'bounces off the x-axis' mean in relation to polynomial graphs?

Back

It means the graph touches the x-axis at that point but does not cross it, indicating an even multiplicity.

Front

What is the process for expanding a polynomial expression?

Back

Use the distributive property to multiply each term and combine like terms.

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 up to n x-intercepts.