Curves of Best Fit

Front

What is a curve of best fit?

Back

A curve of best fit is a line or curve that best represents the data points on a graph, showing the trend of the data.

Front

What is a parabola?

Back

A parabola is a symmetrical curve that is shaped like a U, which can open upwards or downwards, represented by a quadratic equation.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants.

Front

What does it mean for a model to be logarithmic?

Back

A logarithmic model describes a relationship where the rate of change decreases as the value increases, often used for data that grows quickly at first and then levels off.

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over time, represented by the equation f(x) = a(1 + r)^x.

Front

What is the purpose of regression analysis?

Back

Regression analysis is used to determine the relationship between variables and to predict future values based on past data.

Front

What is the significance of the vertex in a parabola?

Back

The vertex is the highest or lowest point of a parabola, representing the maximum or minimum value of the quadratic function.

Front

How do you identify a quadratic function from a set of points?

Back

A quadratic function can be identified if the second differences of the y-values are constant when the x-values are evenly spaced.

Front

What is the difference between linear and quadratic models?

Back

Linear models represent a straight-line relationship, while quadratic models represent a U-shaped curve, indicating a more complex relationship.

Front

What is the general form of a logarithmic function?

Back

The general form of a logarithmic function is f(x) = a log_b(x), where a is a constant and b is the base of the logarithm.