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Identify the center and radius.
3.
x^(2)+(y+2)^(2)=64

Identify the center and radius. $\newline$ $x^{2}+(y+2)^{2}=64$

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. Identify the center and radius.

\newline

x^{2}+(y+2)^{2}=64

Recognize standard form: Step $1$ : Recognize the standard form of a circle's equation. The standard form is $(x - h)^2 + (y - k)^2 = r^2$ , where $(h, k)$ is the center and $r$ is the radius. Given equation: $x^2 + (y+2)^2 = 64$
Compare with standard form: Step $2$ : Compare the given equation with the standard form to find $h$ , $k$ , and $r$ . From $x^2 + (y+2)^2 = 64$ , we can see it matches $(x - 0)^2 + (y + 2)^2 = 64$ . Thus, $h = 0$ , $k = -2$ .
Identify radius: Step $3$ : Identify the radius. $\newline$ The radius squared, $r^2$ , is $64$ . $\newline$ To find $r$ , take the square root of $64$ : $r = \sqrt{64} = 8$ .

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