Linear, Quadratic, or Exponential? Graphs & Equations

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 f(x) = 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 f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

How can you identify a linear function from its graph?

Back

A linear function will produce a straight line when graphed. It has a constant rate of change.

Front

How can you identify a quadratic function from its graph?

Back

A quadratic function will produce a parabolic shape (U-shaped) when graphed. It can open upwards or downwards.

Front

How can you identify an exponential function from its graph?

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An exponential function will show rapid growth or decay, producing a curve that increases or decreases sharply.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does the vertex of a quadratic function represent?

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The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the difference between linear and quadratic functions?

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Linear functions have a constant rate of change and graph to a straight line, while quadratic functions have a variable rate of change and graph to a parabola.

Front

What is the general shape of an exponential function's graph?

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The graph of an exponential function increases or decreases rapidly, showing a J-shaped curve.