M. Alg II HW ck 5-1 B (NB 4-1)

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the definition of a quadratic function?

Back

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

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. It can be found using the formula x = -b/(2a) for the quadratic function f(x) = ax² + bx + c.

Front

How do you determine if a function is linear or quadratic?

Back

To determine if a function is linear or quadratic, analyze its equation. If it is of the form f(x) = mx + b, it is linear. If it is of the form f(x) = ax² + bx + c, it is quadratic.

Front

What is the significance of the linear term in a polynomial?

Back

The linear term in a polynomial indicates the slope of the function and affects the direction and steepness of the graph. It is the term with the first degree (x) in the polynomial.

Front

What does the notation P' represent in calculus?

Back

P' represents the derivative of the function P, which indicates the rate of change of P with respect to its variable.

Front

What is the general form of a quadratic equation?

Back

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

Front

How can you find the vertex of a quadratic function?

Back

The vertex of a quadratic function can be found using the formula (h, k), where h = -b/(2a) and k = f(h). This point represents the maximum or minimum of the parabola.

Front

What is the difference between a linear equation and a quadratic equation?

Back

A linear equation represents a straight line and has a degree of 1, while a quadratic equation represents a parabola and has a degree of 2.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A and B are not both zero.