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$Find the zeros of the function. Enter the solutions from least to greatest. {:[f(x)=(x-2)^(2)-9],[" lesser "x=◻],[" greater "x=◻]:}$

Find the zeros of the function. Enter the solutions from least to greatest. $\newline$ $\begin{array}{l} f(x)=(x-2)^{2}-9 \\ \text { lesser } x= \square \\ \text { greater } x=\square \end{array}$

Full solution

Q. Find the zeros of the function. Enter the solutions from least to greatest.

\newline

\begin{array}{l} f(x)=(x-2)^{2}-9 \\ \text { lesser } x= \square \\ \text { greater } x=\square \end{array}

Set Function Equal to Zero: Set the function equal to zero to find its zeros. $f(x) = (x - 2)^2 - 9 = 0$
Solve Quadratic Equation: Solve the quadratic equation. $\newline$ $(x - 2)^2 = 9$
Take Square Root: Take the square root of both sides of the equation. $\newline$ $\sqrt{(x - 2)^2} = \pm\sqrt{9}$ $\newline$ $x - 2 = \pm3$
Solve for Positive Root: Solve for $x$ by adding $2$ to both sides of the equation. $\newline$ For the positive root: $\newline$ $x - 2 + 2 = 3 + 2$ $\newline$ $x = 5$
Solve for Negative Root: Solve for $x$ using the negative root. $x - 2 + 2 = -3 + 2$ $x = -1$