Algebra 2 Quadratic Regression

Front

What is a quadratic function?

Back

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

Front

What does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

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 the significance of the 'a' value in a quadratic function?

Back

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

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 (b² - 4ac) indicates the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

Front

How can you determine if a quadratic function is a good fit for a set of data?

Back

You can determine the fit by calculating the correlation coefficient (R²) or by visually inspecting the scatter plot and the fitted curve.

Front

What is quadratic regression?

Back

Quadratic regression is a statistical method used to model the relationship between a dependent variable and an independent variable using a quadratic equation.

Front

What is the purpose of using a quadratic model in real-world applications?

Back

Quadratic models are used to describe relationships that exhibit a parabolic trend, such as projectile motion, profit maximization, and population growth.