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Concept

# Zero - Function

To find where a function intercepts the $x$-axis, the function can be set equal to zero. Then, the $x\text{-}$values that satisfy the equation are the zeros of the function, also called the roots. \begin{aligned} f(x) =&\ 2x+1 \\ 0 =&\ 2x+1 \\ x =&\ \text{-}0.5 \end{aligned} This example function has the zero $x=\text{-}0.5,$ since $f(\text{-}0.5)=0.$ Functions whose degree is greater than one, such as quadratic functions, may have more than one root. $\begin{gathered} f(x)=x^2-4 \end{gathered}$ This function has the zeros $x=2$ and $x=\text{-}2,$ since the function will evaluate to $0$ if either of these values is substituted for $x.$ $\begin{array}{c|c} f(x)=x^2-4 & f(x)=x^2-4\\ f(2)=2^2-4 & f(\text{-}2)=(\text{-}2)^2-4 \\ f(2)=0 & f(\text{-}2)=0 \end{array}$ If a given function doesn't intercept the $x$-axis, there will be no solution when the function is equal to $0.$