Quadratic Regression

Front

What is a quadratic regression?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is: f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the 'a' coefficient in a quadratic equation indicate?

Back

The 'a' coefficient determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

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 x-coordinate of the vertex in a quadratic equation?

Back

The x-coordinate of the vertex can be found using the formula: x = -b/(2a).

Front

What does the y-coordinate of the vertex represent in a quadratic function?

Back

The y-coordinate of the vertex represents the maximum or minimum value of the quadratic function.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, representing the value of the function when x = 0.

Front

What is the significance of the x-intercepts in a quadratic function?

Back

The x-intercepts are the points where the graph intersects the x-axis, representing the values of x for which the function equals zero.

Front

How can you determine the maximum height of a projectile using a quadratic function?

Back

The maximum height can be found by evaluating the y-coordinate of the vertex of the quadratic function.

Front

What is the quadratic formula?

Back

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