Chapter 2 Precalculus Assessment Part 1

Front

What is the axis of symmetry for a quadratic function in the form f(x) = a(x-h)^2 + k?

Back

The axis of symmetry is the vertical line x = h.

Front

How do you find the zeros of a cubic function?

Back

Set the function equal to zero and solve for x. The zeros are the x-values where the graph intersects the x-axis.

Front

What is the significance of R^2 in quadratic regression?

Back

R^2 indicates the proportion of variance in the dependent variable that can be explained by the independent variable(s). A value closer to 1 indicates a better fit.

Front

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

Back

For a quadratic function f(x) = ax^2 + bx + c, the vertex can be found using the formula x = -b/(2a).

Front

What is the general form of a cubic function?

Back

The general form of a cubic function is f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have at most n real zeros.

Front

How do you perform quadratic regression using a graphing calculator?

Back

Input the data points into the calculator, select the quadratic regression option, and the calculator will provide the quadratic equation and R^2 value.

Front

What is the formula for the axis of symmetry of the parabola given by f(x) = ax^2 + bx + c?

Back

The axis of symmetry is given by x = -b/(2a).

Front

What is a cubic function with zeros at -2, 1, and 3?

Back

The cubic function is f(x) = (x + 2)(x - 1)(x - 3) = x^3 - 2x^2 - 5x + 6.

Front

What is the vertex form of a quadratic function?

Back

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