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

F(x)=(2x+9)^(2)-32

Find the zeros of the following quadratic function using the square root method. What are the $x$ -intercepts of the graph of the function? $\newline$ $F(x)=(2 x+9)^{2}-32$

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Quadratic equation with complex roots

Full solution

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

x

-intercepts of the graph of the function?

\newline

F(x)=(2 x+9)^{2}-32

Set Function Equal to Zero: Set the function equal to zero to find the x-intercepts. $\newline$ $F(x) = (2x + 9)^2 - 32 = 0$
Isolate Squared Term: Isolate the squared term to use the square root method. $\newline$ $(2x + 9)^2 = 32$
Take Square Root: Take the square root of both sides of the equation. $\newline$ $\sqrt{(2x + 9)^2} = \pm\sqrt{32}$ $\newline$ $2x + 9 = \pm\sqrt{32}$
Simplify Square Root: Simplify the square root of $32$ . $\newline$ $\sqrt{32} = \sqrt{(16 \times 2)} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}$ $\newline$ $2x + 9 = \pm 4\sqrt{2}$
Subtract and Isolate: Subtract $9$ from both sides to isolate the term with $x$ . $\newline$ $2x = -9 \pm 4\sqrt{2}$
Divide to Solve: Divide both sides by $2$ to solve for $x$ . $x = \frac{-9 \pm 4\sqrt{2}}{2}$
Write Solutions: Write the solutions as two separate x-intercepts. $\newline$ $x = \frac{-9 + 4\sqrt{2}}{2}$ and $x = \frac{-9 - 4\sqrt{2}}{2}$

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