SOLUTION: The height h(in feet) of a model rocket in flight is modeled by h(x) = -5/6x2 + 20x, where x is the horizontal distance from the launch point of the rocket (also in feet). Find the

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The height h(in feet) of a model rocket in flight is modeled by h(x) = -5/6x2 + 20x, where x is the horizontal distance from the launch point of the rocket (also in feet). Find the      Log On


   

Question 1002955: The height h(in feet) of a model rocket in flight is modeled by h(x) = -5/6x2 + 20x, where x is the horizontal distance from the launch point of the rocket (also in feet). Find the maximum height of the rocket and determine the horizontal distance from the launch point to where the rocket will land.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the x-coordinate of the vertex is
+x%5Bv%5D+=+-b%2F%282a%29+
Your equation is:
+h%28x%29+=+-%285%2F6%29%2Ax%5E2+%2B+20x+
+a+=+-5%2F6+
+b+=+20+
+-b%2F%282a%29+=+-20%2F%28-10%2F6%29+
+-b%2F%282a%29+=+20%2A%28+6%2F10+%29+
+-b%2F%282a%29+=+12+
Plug this result back into equation to get +h%2812%29+
+h%2812%29+=+-%285%2F6%29%2A12%5E2+%2B+20%2A12+
+h%2812%29+=+-%285%2F6%29%2A144+%2B+240+
+h%2812%29+=+-120+%2B+240+
+h%2812%29+=+120+
The max height is 120 ft
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The horizontal distance from the launch point will
be double +x%5Bv%5D+
+2%2Ax%5Bv%5D+=+2%2A12+
+2%2Ax%5Bv%5D+=+24+
24 ft
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Here's the plot:
+graph%28+400%2C+400%2C+-3%2C+30%2C+-20%2C+140%2C+-%285%2F6%29%2Ax%5E2+%2B+20x+%29+