Question

write an equation that represents the graph of the circle in standard form. the equation of the circle in standard form is

Explanation:

Step1: Find the center of the circle

The center of the circle \((h,k)\) is \((0, - 0.5)\) (by observing the graph where the center is located).

Step2: Find the radius of the circle

The radius \(r\) is \(6.5\) (distance from the center to a point on the circle, for example, from \((0,-0.5)\) to \((6,-0.5)\) is \(6\) units, and considering the grid - based measurement accurately).

Step3: Use the standard form of the circle equation

The standard form of a circle equation is \((x - h)^{2}+(y - k)^{2}=r^{2}\). Substituting \(h = 0\), \(k=-0.5\), and \(r = 6.5\) into the equation:

$$
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$$

Answer:

\(x^{2}+(y + 0.5)^{2}=42.25\)