Solve over the Interval y=100-x^2 , [-10,10]

Problem

y=100−x2,[−10,10]

Solution

1. Identify the task as finding the values of the function y over the specified interval [−10,10]

2. Determine the vertex of the parabola by noting it is in the form y=a*x2+c where a=−1 and c=100

3. Calculate the maximum value, which occurs at x=0 since the parabola opens downward.

y=100−(0)2

y=100

4. Evaluate the endpoints of the interval to find the minimum values.

y=100−(−10)2

y=0

y=100−(10)2

y=0

5. Determine the range by observing that the function is continuous and moves from 0 to 100 and back to 0 over the interval.

Final Answer

y∈[0,100]

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