How long will it take for ball to hit the ground with the equation h=-t^2+10t+22

  about 11.856 time units

Step-by-step explanation:

We have to assume the equation has something to do with the path of the ball relative to the ground. Perhaps it represents height, with t representing time. The height (h) will be zero for the values of t that satisfy ...

  0 = -t^2 +10t +22

Using the quadratic formula, we can find the values of t that satisfy this equation:

  t = (-10 ±√(10² -4(-1)(22)))/(2(-1)) = (-10 ±√188)/-2 = 5±√47

The value of h is zero for t ≈ 11.856.

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About the quadratic formula

The quadratic formula tells you the solution to ...

  ax^2 +bx +c = 0

is given by ...

  x = (-b ±√(b^2 -4ac))/(2a)

Matching this form to the given equation, we see a=-1, b=10, c=22. The variable used in the given equation is t, instead of x.

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step-by-step explanation: