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The path of water from sprinkler is modeled by h(d) = -2*d^2 + 6*d + 4 where h(d) is the height of the water in feet at a distance of d feet from the jet. How far from the sprinkler does the water hit the ground.

Answer :

Luv2Teach

Answer:

Step-by-step explanation:

When the water hits the ground, the height of it is 0.  So replace h(d) with 0 and factor the quadratic.  I used the quadratic formula:

[tex]d=\frac{-6+/-\sqrt{36-4(-2)(4)} }{-4}[/tex] so

[tex]d=\frac{-6+/-\sqrt{36+32} }{-4}[/tex] and

[tex]d=\frac{-6+/-\sqrt{68} }{-4}[/tex] which gives us the two distances as

[tex]d=\frac{-6+\sqrt{68} }{-4}[/tex]  and  [tex]d=\frac{-6-\sqrt{68} }{-4}[/tex]

The first case gives us a distance of -.56155 feet and the second a distance of 3.56155 feet.  Since distance will never be negative, then

d = 3.56 feet

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