To find the maximum height that the rabbit can reach during its jump, we need to determine the vertex of the parabolic function. The vertex is given by the formula x = -b/2a, where a and b are coefficients of x in the equation y = ax^2 + bx + c.
In the given equation y = -0.296x^2 + 2.7x, a = -0.296 and b = 2.7. Plugging these values into the formula, we get:
x = -(2.7) / (2*(-0.296))
x = -2.7 / -0.592
x = 4.563
Now that we have the x-coordinate of the vertex, we can substitute it back into the equation to find the maximum height:
y = -0.296(4.563)^2 + 2.7(4.563)
y = -0.296(20.830) + 12.337
y = -6.157 + 12.337
y = 6.18
Therefore, the maximum height that the rabbit can reach during its jump is 6.18 centimeters.
To find the total length of the jump, we need to find the x-coordinate where y is equal to zero (since that indicates when the rabbit reaches the ground). We can solve the equation -0.296x^2 + 2.7x = 0 by factoring out x:
x(-0.296x + 2.7) = 0
This equation is satisfied when either x = 0 or -0.296x + 2.7 = 0. Solving the second equation, we get:
-0.296x = -2.7
x = -2.7 / -0.296
x = 9.12
Therefore, the rabbit's jump covers a total length of 9.12 centimeters.
The function y = -0.296x^2 + 2.7x models the length x and height y that your sister's pet rabbit can jump, in centimeters. What is the maximum height that the rabbit can reach during its jump? Once the rabbit reaches the ground, what is the total length of its jump?
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