Mike D. answered • 05/18/21

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(a) If 1 unit on the x axis is 1 ft then the parabola goes through the points (0,0), (630,0) and (315, 630)

[ the vertex has y = 630 and is halfway between the zeroes ]

So the vertex is (h,k) h = 315 k = 630

Equation is y = a (x-h)^{2} + k = a (x-315)^{2} + 630

x = 0 y = 0 so a (315)^{2} + 630 = 0 so a = - 630 / 315^{2}

y = (-630/315^{2}) (x-315)^{2} + 630

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(b) Draw the function on Desmos

Draw the line y=100

Find the x values at the 2 points of intercept

Find the difference of these x values

(c) Draw x = 75

Find the y value where this intercepts the parabola

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(d) Draw y = 400

Find the x coordinate of one of the points of intersection with the parabola

Calculate (x-315) and take the absolute value of this