How do you compute the x and y intercepts of a quadratic function?

For the x intercepts, set y to zero,and solve for x. For the x intercepts, set y to zero and solve for x.

To compute the x-intercepts of a quadratic function, you need to solve for the values of x where the graph of the function intersects the x-axis. The x-intercepts are also known as the roots or zeros of the quadratic equation.

To find the x-intercepts, you can set the y-coordinate of the function to zero and then solve for the corresponding values of x.

Let's assume your quadratic function is in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

1. Set y to zero: f(x) = 0.
2. Replace f(x) with 0 in the quadratic equation: ax^2 + bx + c = 0.
3. Next, solve this quadratic equation by factoring, using the quadratic formula, completing the square, or any other appropriate method.
4. Once you have the solutions for x, those values will be the x-intercepts of the quadratic function.

For example, consider the quadratic function f(x) = 2x^2 - 5x + 3.

1. Set y to zero: 2x^2 - 5x + 3 = 0.
2. Solve this quadratic equation using factoring, the quadratic formula, or any other appropriate method.
In this case, you can factor it as (2x - 3)(x - 1) = 0.
3. Apply the zero product property, which states that if a*b = 0, then either a = 0 or b = 0.
So, either (2x - 3) = 0 or (x - 1) = 0.
4. Solve each equation separately:
- For (2x - 3) = 0, you get x = 3/2 or x = 1.5.
- For (x - 1) = 0, you get x = 1.
Therefore, the x-intercepts of the quadratic function f(x) = 2x^2 - 5x + 3 are x = 1.5 and x = 1.

Remember, the number of x-intercepts can vary depending on the quadratic function. It can have two distinct x-intercepts, one repeated x-intercept, or none at all, depending on the discriminant of the equation.