Graph y = square root of 16-x^2

Problem

y=√(,16−x2)

Solution

1. Identify the type of equation by squaring both sides to remove the radical.

y2=16−x2

2. Rearrange the equation into the standard form of a circle by adding x2 to both sides.

x2+y2=16

3. Determine the geometric properties of the circle, where the center is (0,0) and the radius is r=√(,16)=4

x2+y2=4

4. Consider the restriction imposed by the original square root function, which requires y≥0

y=√(,16−x2)≥0

5. Define the domain by ensuring the radicand is non-negative, 16−x2≥0 which simplifies to |x|≤4

−4≤x≤4

6. Conclude that the graph is the upper half (semicircle) of a circle centered at the origin with a radius of 4.

Graph: Semicircle from *x=−4* to *x=4

Final Answer

y=√(,16−x2)⇒Upper semicircle centered at *(0,0)* with radius *4

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