Math

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The path of a cliff diver as he dives into a lake is given by the equation
y= -(x-10)^2+75, where y meters is the divers height above the water and x meters is the horizontal distance travelled by the diver. What is the maximum hight the diver is above water?

Is the answer to this question 75 meters? This is how I worked it out, please verify if correct:

parabola opens down

axis of symetry is 10 (h=10)

therefore y=-1(10-10)^2 + 75 = 75

Please is this right?

• Math -

check with calculus
dy/dx = 2(x-10)
0 at max so x = 10
y = (10-10)^2 + 75
y = 75 sure enough

• Math -

Many thanks

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