Understanding X-Intercepts | Finding the Points of Intersection with the X-Axis in Mathematics

X intercepts

In mathematics, the x-intercepts of a function represent the points where the graph of the function intersects the x-axis

In mathematics, the x-intercepts of a function represent the points where the graph of the function intersects the x-axis. These points have a y-coordinate of zero because they lie on the x-axis. From a graphical perspective, x-intercepts are the values of x for which the corresponding y-values are equal to zero.

To find the x-intercepts of a function algebraically, you need to set the y-value (or the function itself) equal to zero and solve for x. Consider a function f(x), setting f(x) = 0 will give you the equation:

f(x) = 0

Then, you can solve this equation to find the values of x where the function intersects the x-axis. The solutions to this equation will give you the x-coordinate(s) of the x-intercept(s).

For example, let’s take the function f(x) = x^2 – 4. To find the x-intercepts, we set f(x) equal to zero:

x^2 – 4 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, factoring is possible:

(x – 2)(x + 2) = 0

By setting each factor equal to zero, we get two equations:

x – 2 = 0 -> x = 2
x + 2 = 0 -> x = -2

So, the x-intercepts of the function f(x) = x^2 – 4 are x = 2 and x = -2. These are the points where the graph of the function crosses the x-axis.

Remember, an equation may have zero, one, or multiple x-intercepts.

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