$\"\"$

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The center of the parabola is at the origin.

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(a) Find the equation of the parabola.

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The equation of the parabola is $\"\"$ .

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The deflection of the beam at its center is $\"\"$ .

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The point on the parabola is at $\"\"$ .

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The parabola passes through the point $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Therefore, the equation of the parabola is $\"\"$ .

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$\"\"$

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(b) How far from the center of the beam is the deflection $\"\"$ .

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The equation of the parabola is $\"\"$ .

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When the deflection is $\"\"$ then $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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When the distance is $\"\"$ , the center of the beam deflection is $\"\"$ .

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$\"\"$

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(a) The equation of the parabola is $\"\"$ .

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(b) When the distance is $\"\"$ , the center of the beam deflection is $\"\"$ .