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: Determine the center of the circle

The center of the circle \((h,k)\) is \((- 1,0)\) from the graph.

Step2: Determine the radius of the circle

The radius \(r\) is the distance from the center \((-1,0)\) to a point on the circle. Using the distance formula or counting units on the grid, \(r = 3\).

Step3: Use the standard form of the circle equation

The standard form of a circle equation is \((x - h)^{2}+(y - k)^{2}=r^{2}\). Substitute \(h=-1,k = 0,r = 3\) into the formula: \((x-(-1))^{2}+(y - 0)^{2}=3^{2}\), which simplifies to \((x + 1)^{2}+y^{2}=9\).

Answer:

\((x + 1)^{2}+y^{2}=9\)