Find the x and y Intercepts y=x square root of 4-x^2

Problem

y=x√(,4−x2)

Solution

1. Find the y-intercept by setting x=0 in the equation.

y=0√(,4−0)

y=0

2. Find the x-intercepts by setting y=0 and solving for x

0=x√(,4−x2)

3. Apply the zero product property to set each factor equal to zero.

x=0

√(,4−x2)=0

4. Solve the radical equation by squaring both sides.

4−x2=0

x2=4

x=±2

5. Verify the domain to ensure the intercepts are valid. The expression under the square root must be non-negative: 4−x2≥0 which means −2≤x≤2 All found values (0, 2, -2$) are within this domain.

Final Answer

x-intercepts: *(−2,0),(0,0),(2,0); y-intercept: *(0,0)

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