Linear, Quadratic, and Exponential Functions Flashcard

Front

What is a parabola that opens down?

Back

A parabola that opens down has a negative leading coefficient in its quadratic equation, such as f(x) = -x² + bx + c.

Front

How do you identify a quadratic function?

Back

A quadratic function is identified by its standard form f(x) = ax² + bx + c, where a ≠ 0.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = ab^x, where a is a constant and b is the base.

Front

What does it mean for a function to be linear?

Back

A linear function has a constant rate of change and can be represented by the equation y = mx + b.

Front

How can you tell if a table of values represents a linear function?

Back

A table represents a linear function if the differences between consecutive y-values are constant.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have a constant slope and graph as a straight line, while quadratic functions have a variable slope and graph as a parabola.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens up or down.

Front

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

Back

The y-intercept of a linear function can be found by setting x = 0 in the equation y = mx + b.

Front

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

Back

The leading coefficient determines the direction in which the parabola opens: positive for up, negative for down.