Linear, Exponential, Quadratic: Which is it?

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What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. Example: Population growth.

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What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. Example: Radioactive decay.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation 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, represented by the equation y = ax² + bx + c, where a, b, and c are constants.

Front

How can you identify an exponential function from a table of values?

Back

An exponential function will show a constant ratio between consecutive values, indicating multiplicative growth or decay.

Front

What is the general form of an exponential function?

Back

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

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What does the graph of a linear function look like?

Back

The graph of a linear function is a straight line that can slope upwards or downwards depending on the sign of the slope.

Front

What does the graph of a quadratic function look like?

Back

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

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much faster growth over time.

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 whether it opens upwards or downwards.