Finite Differences Graded

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 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 function that can be represented by a parabola. It has the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

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

Back

To determine if a table represents a linear function, check if the differences between consecutive y-values are constant.

Front

How can you determine if a table of values represents a quadratic function?

Back

To determine if a table represents a quadratic function, check if the second differences of the y-values are constant.

Front

What does it mean if a table of values is classified as 'neither'?

Back

If a table is classified as 'neither', it means that the relationship between the x and y values does not fit the patterns of linear or quadratic functions.

Front

What is the first difference in a set of values?

Back

The first difference is the difference between consecutive y-values in a table of values.

Front

What is the second difference in a set of values?

Back

The second difference is the difference of the first differences, calculated to determine if the relationship is quadratic.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function; it shows how much y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the value of y when x is 0; it represents the point where the line crosses the y-axis.

Front

Can a quadratic function have a negative leading coefficient?

Back

Yes, a quadratic function can have a negative leading coefficient, which will result in a parabola that opens downwards.