Linear, Exponential, and Quadratic Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

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 (a positive real number), and x is the exponent. It shows rapid growth or decay.

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. Its graph is a parabola.

Front

How do you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values. The differences in y-values divided by the differences in x-values will be the same.

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis. It occurs when x = 0.

Front

How can you determine if a function is exponential from a table of values?

Back

An exponential function will show a constant multiplicative rate of change. The ratio of consecutive y-values will remain constant.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

What is the general shape of a quadratic function's graph?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient a.

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while quadratic functions have a variable rate of change and graph as parabolas.

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form y = ax^2 + bx + c can be found using the formula x = -b/(2a). Substitute x back into the function to find y.