Linear, Quadratic, and Exponential Data Models

Front

What type of function has constant second differences?

Back

Quadratic function.

Front

How can you determine if a table of values represents a linear, quadratic, or exponential function?

Back

By analyzing the differences between the values: constant first differences indicate linear, constant second differences indicate quadratic, and a constant ratio indicates exponential.

Front

What is the general form of a linear function?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the general form of a quadratic function?

Back

y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the general form of an exponential function?

Back

y = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

What is the difference between linear and quadratic functions in terms of their graphs?

Back

Linear functions graph as straight lines, while quadratic functions graph as parabolas.

Front

What are the characteristics of an exponential function's growth?

Back

Exponential functions grow rapidly and their rate of increase becomes faster as x increases.

Front

What does it mean for a function to be quadratic?

Back

It means the function can be represented by a polynomial of degree 2, which has a parabolic shape.

Front

How can you identify a quadratic function from a set of data points?

Back

By plotting the points and checking if they form a parabolic shape or by calculating the second differences.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.