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Mathematics 64 Online
OpenStudy (anonymous):

MEDAL PLUS FAN 4 HELP PLZZZZZZZZZZ A golfer hits the golf ball. The quadratic y = -10⋅x2 + 60⋅x gives the time x seconds when the golf ball is at height 0 feet. In total, how long is the golf ball in the air?

OpenStudy (anonymous):

@kirbykirby plz help

OpenStudy (anonymous):

Thank youuuuuuuuuuuuuu

OpenStudy (kirbykirby):

This is essentially the equation of a parabola. Since you have a negative coefficient infront of \(x^2\), the parabola looks something like this: |dw:1400721300064:dw| It is symmetric, so when the golfball leaves the ground and reaches the vertex of the parabola, it will take the same amount of time to leave the vertex and reach the ground again. So, if you can find the zero of the parabola (i.e. when y = 0), then this indicates how much time the ball travelled, since x tells you the time the ball travels. \[-10x^2+60x=0\\ 10x(-x+6)=0\] So, \(x=0\) or \(-x+6=0\implies x=6\) \(x=0\) is just the starting time, so \(x=6\) is the amount of time, in seconds, for it to take to leave the ground and reach the ground again further away.

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