Chapter 1 Review

Front

What is the vertex of the function f(x) = 2|x - 4|?

Back

The vertex is (4, 0). The vertex of an absolute value function f(x) = a|x - h| + k is at the point (h, k).

Front

What does the equation x - 2y < -6 represent graphically?

Back

It represents a region on the coordinate plane where the line x - 2y = -6 is a boundary. The area below this line is included in the solution set.

Front

How do you find the vertex of a quadratic function in the form f(x) = ax^2 + bx + c?

Back

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting this value back into the function to find the y-coordinate.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line as if it were an equation. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) has exactly one output (y-value).

Front

What is the standard form of a quadratic function?

Back

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

Front

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

Back

A function is increasing on an interval if the y-values rise as x-values increase. It is decreasing if the y-values fall as x-values increase.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.