Activity on Quadratic Regression

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form of f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the term 'curve of best fit' mean?

Back

The 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

How do you determine the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form f(x) = ax² + bx + c can be found using the formula x = -b/(2a). The y-coordinate can be found by substituting this x value back into the function.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant, given by b² - 4ac, indicates the nature of the roots: if > 0, there are two real roots; if = 0, there is one real root; if < 0, there are no real roots.

Front

How can you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex, which can be found using x = -b/(2a). Substitute this x value into the function to find the corresponding y value.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What is the purpose of quadratic regression?

Back

Quadratic regression is used to model the relationship between a dependent variable and an independent variable by fitting a quadratic equation to the data.