Quadratic and Exponential - Curve of Best Fit - Flashcard

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting this value back into the function to find the y-coordinate.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

What is the difference between quadratic and exponential functions?

Back

Quadratic functions have a degree of 2 and their graphs are parabolas, while exponential functions have a variable exponent and their graphs show rapid growth or decay.

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 in a scatter plot, often determined using regression analysis.

Front

What is linear regression?

Back

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.