Finding x-intercepts | A step-by-step guide and examples for finding the points where a function intersects the x-axis.

x-intercepts of f(x)

The x-intercepts of a function f(x) are the points where the graph of the function intersects the x-axis

The x-intercepts of a function f(x) are the points where the graph of the function intersects the x-axis. In other words, they are the values of x for which f(x) equals zero.

To find the x-intercepts, you can set f(x) equal to zero and solve for x. This is done by setting up an equation f(x) = 0 and using algebraic techniques to isolate x.

For example, consider the quadratic function f(x) = x^2 – 4x + 3. To find its x-intercepts, you would set f(x) equal to zero:

x^2 – 4x + 3 = 0

Now, you can factor the quadratic expression (if possible) or use the quadratic formula to solve for x.

In this case, the quadratic expression cannot be factored easily, so you can use the quadratic formula:

x = (-b ± √(b^2 – 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation. For our example, a = 1, b = -4, and c = 3. Plugging these values into the quadratic formula, you get:

x = (-(-4) ± √((-4)^2 – 4(1)(3))) / (2(1))
= (4 ± √(16 – 12)) / 2
= (4 ± √4) / 2
= (4 ± 2) / 2

This gives two possible values for x:

x = (4 + 2) / 2 = 6 / 2 = 3
x = (4 – 2) / 2 = 2 / 2 = 1

So, the x-intercepts of the function f(x) = x^2 – 4x + 3 are x = 1 and x = 3.

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