To find the x-intercept of a quadratic function, you need to determine the points where the graph of the function crosses the x-axis. The x-intercept occurs when the value of the function is zero. Essentially, you are looking for the values of x that make the equation true when set to zero.
Here’s a step-by-step process to find the x-intercept:
- Set the quadratic function equal to zero: If your quadratic function is in the form of f(x) = ax² + bx + c, you would set it up as:
- ax² + bx + c = 0
- Solve for x: You can solve the quadratic equation using different methods, such as factoring, completing the square, or using the quadratic formula x = (-b ± √(b² – 4ac)) / 2a. The quadratic formula is especially useful when factoring is difficult.
- Calculate values: Plug in the values of a, b, and c into the formula to find the possible values of x that satisfy the equation.
- Identify the x-intercepts: The solutions you get from the equation are your x-intercepts. If there are two solutions, the parabola crosses the x-axis at two points; if there is one solution, the vertex of the parabola touches the x-axis; and if there are no real solutions, the parabola does not cross the x-axis.
For example, consider the quadratic function f(x) = x² – 4. Setting the equation equal to zero:
x² – 4 = 0
Factoring gives us:
(x – 2)(x + 2) = 0
This provides two solutions: x = 2 and x = -2. Therefore, the x-intercepts of the function are at the points (2, 0) and (-2, 0).
In summary, finding the x-intercept involves solving the quadratic equation for zero and determining the corresponding x-values.