Identifying Function Families

Front

What is a root of a function?

Back

A root of a function is a value of x for which the function equals zero, meaning the graph intersects the x-axis.

Front

Identify the x-intercept of the function y = 2x - 8.

Back

The x-intercept is the point where y = 0. For y = 2x - 8, set 0 = 2x - 8, which gives x = 4. So, the x-intercept is (4, 0).

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a*b^x, where b is a positive constant and a is a non-zero constant.

Front

Factor the expression x^2 - 25.

Back

The factored form is (x + 5)(x - 5).

Front

What type of function is y = x^2 + 3?

Back

This is a quadratic function because it can be expressed in the form y = ax^2 + bx + c.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting back to find the y-coordinate.

Front

What is the difference between a linear and a quadratic function?

Back

A linear function has a constant rate of change and graphs to a straight line, while a quadratic function has a variable rate of change and graphs to a parabola.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax^2 + bx + c.