Linear, Absolute Value, & Quadratic Functions Review

Front

What is the general form of a linear function?

Back

A linear function can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros of a quadratic function f(x) = ax^2 + bx + c, set f(x) = 0 and solve the equation using factoring, the quadratic formula, or completing the square.

Front

What does the absolute value function represent?

Back

The absolute value function, denoted as f(x) = |x|, represents the distance of x from 0 on the number line, always yielding a non-negative result.

Front

What is the effect of a negative coefficient in front of an absolute value function?

Back

A negative coefficient in front of an absolute value function, such as f(x) = -a|x - h| + k, reflects the graph across the x-axis.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola (upward or downward).

Front

How do you determine the intervals where a function is greater than zero?

Back

To determine where a function f(x) > 0, find the zeros of the function, then test intervals between the zeros to see where the function is positive.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the zeros of a quadratic equation and is given by x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing on an interval if the output values rise as the input values increase, and decreasing if the output values fall as the input values increase.