x-intercept
In mathematics, an x-intercept is a point where a graph intersects or crosses the x-axis
In mathematics, an x-intercept is a point where a graph intersects or crosses the x-axis. It is the x-coordinate of the point where the graph intersects the x-axis.
To find the x-intercept of a graph, we need to determine the value of x when the y-coordinate is zero. In other words, we are looking for the point(s) where the graph intersects the x-axis, which is the line with a y-coordinate of zero.
For example, let’s consider the equation of a line: y = mx + b, where m is the slope and b is the y-intercept. To find the x-intercept, we set y = 0 and solve the equation for x.
0 = mx + b
Solving for x, we get:
mx = -b
x = -b/m
This gives us the x-coordinate of the x-intercept.
If we have a quadratic equation, like y = ax^2 + bx + c, we can find the x-intercepts by setting y = 0 and solving the quadratic equation for x. This can be done by factoring, completing the square, or using the quadratic formula.
For example, let’s consider the quadratic equation: y = x^2 – 4x + 4. To find the x-intercepts, we set y = 0 and solve:
0 = x^2 – 4x + 4
Factoring the quadratic equation, we get:
0 = (x – 2)^2
Setting each factor equal to zero:
x – 2 = 0
x = 2
From this, we can see that the x-intercept of the graph of the quadratic equation is x = 2.
It’s important to note that not all graphs have x-intercepts. Some graphs may not intersect the x-axis at any point, while others may intersect it at multiple points. The x-intercepts are significant because they provide crucial information about the behavior and solutions of the equation or function.
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