ALL FUNCTIONS

Front

What is the general form of a quadratic equation?

Back

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

Front

What type of function is represented by the equation y = 5x^2 - 4x + 10?

Back

This equation represents a quadratic function.

Front

How can you identify if a function is quadratic?

Back

A function is quadratic if it can be expressed in the form y = ax^2 + bx + c, where a ≠ 0.

Front

What is the difference between linear, exponential, and quadratic functions?

Back

Linear functions have a constant rate of change, exponential functions grow or decay at a constant percentage rate, and quadratic functions have a variable rate of change that forms a parabola.

Front

What is the formula for calculating the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula x = -b/(2a).

Front

What does the 'a' value in a quadratic equation determine?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of the quadratic equation: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

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.

Front

How do you interpret the slope in a linear regression equation?

Back

The slope in a linear regression equation (y = mx + b) represents the change in the dependent variable (y) for a one-unit increase in the independent variable (x).

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = ab^x, where 'a' is a constant, 'b' is the base of the exponential (b > 0), and 'x' is the exponent.