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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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?

Back

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

Tags

CCSS.HSF-IF.C.7E

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?

Back

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?

Back

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?

Back

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

Tags

CCSS.HSF-IF.C.7E