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Concept

Zero - Function

Any input value in the domain of a function whose output equals is known as a zero or root of the function. A function can have more than one zero or no zeros at all. Graphically, the zeros of a function are the coordinates of the intercepts.
The function 0.4*(x+2)*(x-1)*(x-2) with zeros at (-2,0), (1,0), and (2,0)
Consider the following function as an example.
To find the zeros of a function, substitute the for the output in the function rule and solve the resulting equation for
Solve for
This example function has a zero at because This can be verified by evaluating the function at this value.
Evaluate
Since this is the only solution to the equation, it is also the only zero of the function. If a function does not intercept the axis, there will be no real solution for the resulting equation when the function rule is set equal to In such a case, the function will have no zeros.
Zeros of different functions applet
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