Pre Cal Polynomial Functions

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you convert a quadratic expression in standard form to vertex form?

Back

To convert a quadratic expression from standard form (ax² + bx + c) to vertex form, you can complete the square.

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial evaluates to zero.

Front

How do you find the zeros of a polynomial given one factor?

Back

To find the zeros of a polynomial given one factor, set the factor equal to zero and solve for x, then use polynomial division to find the remaining factors.

Front

What does it mean for a root to have a multiplicity?

Back

A root has a multiplicity if it is a solution to the polynomial equation more than once; for example, if (x - r)² is a factor, then r has a multiplicity of 2.

Front

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

Back

The leading coefficient determines the end behavior of the polynomial function; if it is positive, the graph rises to the right, and if negative, it falls to the right.

Front

What is the difference between increasing and decreasing intervals in a function?

Back

An increasing interval is where the function's output values rise as the input values increase, while a decreasing interval is where the output values fall as the input values increase.

Front

How can you determine if a function is increasing or decreasing from its graph?

Back

You can determine if a function is increasing or decreasing by observing the slope of the graph; if the slope is positive, the function is increasing, and if negative, it is decreasing.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is given by y = ax² + bx + c, where a, b, and c are constants.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function is a vertical line that passes through the vertex, given by the equation x = h, where (h, k) is the vertex.