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Find the zeros of the quadratic function using the square root method. What are the
x-intercepts of the graph of the function?

g(x)=(x-3)^(2)-1

Find the zeros of the quadratic function using the square root method. What are the $x$ -intercepts of the graph of the function? $\newline$ $g(x)=(x-3)^{2}-1$

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Quadratic equation with complex roots

Full solution

Q. Find the zeros of the quadratic function using the square root method. What are the

x

-intercepts of the graph of the function?

\newline

g(x)=(x-3)^{2}-1

Set Function Equal to Zero: Set the function equal to zero to find the x-intercepts. $g(x) = (x - 3)^2 - 1 = 0$
Add to Isolate Squared Term: Add $1$ to both sides to isolate the squared term. $\newline$ $(x - 3)^2 = 1$
Apply Square Root Method: Apply the square root method to both sides of the equation to solve for $x$ . $\sqrt{(x - 3)^2} = \pm\sqrt{1}$
Simplify Square Roots: Simplify the square root of the squared term and the square root of $1$ . $x - 3 = \pm 1$
Solve for x: Solve for x by adding $3$ to both sides of the equation. $\newline$ $x = 3 \pm 1$
Write Solutions: Write the two solutions for $x$ . $x = 3 + 1$ or $x = 3 - 1$
Simplify Expressions: Simplify both expressions to find the $x$ -intercepts. $x = 4$ or $x = 2$

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