SOLUTION: A projectile follows a parabolic path whose height, in meters, is given by the function f(x) = -x^2 + 2x +2. Find the maximum horizontal distance that the projectile may cover.

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: A projectile follows a parabolic path whose height, in meters, is given by the function f(x) = -x^2 + 2x +2. Find the maximum horizontal distance that the projectile may cover.       Log On

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Question 828022: A projectile follows a parabolic path whose height, in meters, is given by the function f(x) = -x^2 + 2x +2. Find the maximum horizontal distance that the projectile may cover.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29+=+-x%5E2+%2B+2x+%2B2+
The horizontal distance, x, is
greatest at +f%28x%29+=+0+ where +f%28x%29+
is the height
+-x%5E2+%2B+2x+%2B+2++=+0+
Use the quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-1+
+b+=+2+
+c+=+2+
+x+=+%28+-2+%2B-+sqrt%28+2%5E2+-+4%2A%28-1%29%2A2+%29%29+%2F+%282%2A%28-1%29%29+
+x+=+%28+-2+%2B-+sqrt%28+4+%2B+8+%29%29+%2F+%28-2%29+
+x+=+%28+-2+-+2%2Asqrt%28+3+%29+%29+%2F+%28-2+%29+
+x+=+1+%2B+sqrt%283%29+
+x+=+1+%2B+1.732+
+x+=+2.732+ maximum distance of projectile
Notice that I used the minus square root to get
the greatest possible positive result
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+4%2C+-1%2C+4%2C+-x%5E2+%2B+2x+%2B+2+%29+