Graph y = square root of 9-x^2

Problem

y=√(,9−x2)

Solution

1. Identify the domain of the function by ensuring the expression under the square root is non-negative.

9−x2≥0

x2≤9$$$$−3≤x≤3

2. Square both sides of the equation to identify the shape of the curve.

y2=9−x2

3. Rearrange the equation into a standard form.

x2+y2=9

4. Recognize that this is the equation of a circle centered at (0,0) with a radius of r=√(,9)=3

x2+y2=3

5. Determine the specific portion of the circle to graph. Since the original equation is y=√(,9−x2) the value of y must be greater than or equal to zero.

y≥0

6. Conclude that the graph is the upper semicircle of x2+y2=9 starting at (−3,0) passing through (0,3) and ending at (3,0)

Final Answer

y=√(,9−x2)⇒Upper semicircle of *x2+y2=9

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