Key Features of Linear, Quadratic and Exponential Functions

Front

What is a linear function?

Back

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

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

What does it mean for a function to exhibit growth?

Back

A function exhibits growth when its output increases as the input increases, typically seen in exponential functions.

Front

What does it mean for a function to exhibit decay?

Back

A function exhibits decay when its output decreases as the input increases, commonly seen in exponential decay functions.

Front

How do you find the slope of a linear function?

Back

The slope of a linear function can be found by taking the difference in y-values divided by the difference in x-values between two points on the line.

Front

What are x-intercepts and y-intercepts?

Back

The x-intercept is the point where the graph crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0).

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax^2 + bx + c.

Front

How can you determine the number of solutions of a quadratic equation?

Back

The number of solutions can be determined using the discriminant (b^2 - 4ac). If it's positive, there are 2 solutions; if zero, 1 solution; if negative, no real solutions.