Quadratic Regression

Front

What is the y-intercept in a quadratic function?

Back

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

Front

What does the vertex of a quadratic function represent?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How do you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form of the quadratic equation y = ax^2 + bx + c.

Front

What is the standard form of a quadratic equation?

Back

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

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' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

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 by fitting a quadratic equation to the data.

Front

How do you find the curve of best fit for a set of data points?

Back

To find the curve of best fit, you can use quadratic regression analysis to determine the quadratic equation that minimizes the difference between the observed values and the values predicted by the model.

Front

What is the formula for the vertex of a quadratic function in standard form?

Back

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

Front

What does the x-intercept of a quadratic function represent?

Back

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

Front

How can you identify a quadratic function from a set of data points?

Back

You can identify a quadratic function by observing the pattern of the data points; if they form a parabolic shape when graphed, it suggests a quadratic relationship.