Linear & Quadratic Patterns

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope of a linear function represent?

Back

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

Tags

CCSS.8.EE.B.5

Front

What are first differences in a linear function?

Back

First differences are the differences between consecutive y-values in a linear function. For linear functions, these differences are constant.

Tags

CCSS.HSF-LE.A.1B

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How can you identify a quadratic function from a table of values?

Back

A quadratic function can be identified from a table of values by calculating the second differences, which will be constant.

Front

What type of function is represented by a parabolic graph?

Back

A parabolic graph represents a quadratic function.

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 the direction of the parabola.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the value of y when x = 0.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be expressed in the form y = mx + b, resulting in a straight line when graphed.

Tags

CCSS.8.F.A.3

Front

What is an example of a real-world situation that can be modeled by a linear function?

Back

An example is calculating the total cost of items purchased at a constant price per item.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2