SOLUTION: When a gray kangaroo jumps, its path through the air can be modeled by y= -0.0267x2 + 0.8x where x is the kangaroo's horizontal distance traveled (in feet) wand y is the correspond

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Question 251191: When a gray kangaroo jumps, its path through the air can be modeled by y= -0.0267x2 + 0.8x where x is the kangaroo's horizontal distance traveled (in feet) wand y is the corresponding height (in feet). HOw high can a gray kangaroo jump? How far can it jump?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
When a gray kangaroo jumps, its path through the air can be modeled by:
y = -0.0267x2 + 0.8x where x is the kangaroo's horizontal distance traveled (in feet) wand y is the corresponding height (in feet).
How high can a gray kangaroo jump?
:
y = -0.0267x^2 + 0.8x
:
Find the max height by finding the axis of symmetry; Formula: x = -b/(2a)
In this equation: a = -.0267; b = .8, so we have:
x = %28-.8%29%2F%282%2A-.0267%29
:
x = %28-.8%29%2F%28-.0534%29
x = +14.98; max height occurs at horizontal dist of 14.98 ft
:
Find the max height, replace x with 14.98 in the original equation
y = -0.0267(14.98^2) + 0.8(14.98)
y = -0.026y(224.4) + 11.984
y = -5.99 + 11.984
y ~ 6 ft is max height
:
How far can it jump? When this occurs, y = 0
-0.0267x^2 + 0.8x = 0
Factor out -x
x(.0267x - 0.8) = 0
Two solutions
x = 0; the starting point of the leap
and
.0267x = +.8
x = .8%2F.0267
x = 29.96 ~ 30 ft is the distance he can jump (landing point)
:
:
Would look like this graphically
+graph%28+300%2C+200%2C+-10%2C+35%2C+-5%2C+8%2C+-.0267x%5E2%2B.8x%29+