key term - X-Intercept

Definition

The x-intercept of a graph is the point where the graph of a function or equation crosses the x-axis. It represents the value of x when the function's y-value is zero, indicating the horizontal location where the graph intersects the horizontal axis.

5 Must Know Facts For Your Next Test

1. The x-intercept is a crucial feature when graphing linear equations, as it helps determine the point where the line crosses the horizontal axis.
2. Finding the x-intercept is often necessary when solving systems of linear equations, as the x-intercept of one equation may be the solution to the system.
3. In the context of quadratic functions, the x-intercepts represent the points where the graph crosses the x-axis, which can be found by solving the quadratic equation.
4. The x-intercept can be used to determine the range and domain of a function, as it represents the values of x where the function is equal to zero.
5. Radicals in functions, such as square roots, can also have x-intercepts, which are the values of x where the function is equal to zero.

Review Questions

• Explain how the x-intercept is used when graphing linear equations.
  • When graphing a linear equation in the form $y = mx + b$, the x-intercept represents the point where the line crosses the x-axis, meaning the value of y is zero. This point can be found by setting y = 0 and solving for x, which gives the x-coordinate of the x-intercept. The x-intercept is an important feature of the graph, as it helps determine the range and domain of the function and can be used to solve systems of linear equations.
• Describe the relationship between the x-intercept and the slope of a line.
  • The x-intercept and the slope of a line are closely related. The slope, often denoted as 'm', represents the rate of change between the x and y variables. The x-intercept, on the other hand, represents the value of x when the function's y-value is zero. These two features work together to define the overall shape and position of the line on the graph. For example, a line with a positive slope will have an x-intercept to the left of the y-axis, while a line with a negative slope will have an x-intercept to the right of the y-axis.
• Analyze how the x-intercept is used to graph quadratic functions and solve for their roots.
  • In the context of graphing quadratic functions, the x-intercepts represent the points where the graph crosses the x-axis. These x-intercepts can be found by solving the quadratic equation in the form $ax^2 + bx + c = 0$, where the solutions to this equation give the x-coordinates of the x-intercepts. The x-intercepts are important for understanding the behavior of the quadratic function, as they indicate the values of x where the function is equal to zero. This information can be used to determine the range and domain of the function, as well as to identify the roots or solutions of the quadratic equation.

Related terms

Y-Intercept: The y-intercept of a graph is the point where the graph of a function or equation crosses the y-axis. It represents the value of y when the function's x-value is zero, indicating the vertical location where the graph intersects the vertical axis.

Slope:

The slope of a line is a measure of the steepness of the line, representing the rate of change between the x and y variables. It is often denoted by the letter 'm' and is calculated as the change in y divided by the change in x.

Linear Equation:

A linear equation is an equation that represents a straight line on a graph. It can be expressed in the form $y = mx + b$, where 'm' is the slope and 'b' is the y-intercept.