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? (1 point) Responses 2.7 cm high; 0.296 cm long 2.7 cm high; 0.296 cm long 6.2 cm high; 9.1 cm long 6.2 cm high; 9.1 cm long 4.6 cm high; 6.2 cm long 4.6 cm high; 6.2 cm long 9.1 cm high; 6.2 cm long
To find the maximum height that the rabbit can reach, we need to find the vertex of the parabolic function y = -0.296x^2 + 2.7x. The x-coordinate of the vertex is given by:
x = -b / (2a) = -2.7 / (2*(-0.296)) = 4.55
Now, we can plug this x-coordinate back into the function to find the maximum height:
y = -0.296(4.55)^2 + 2.7(4.55) ≈ 6.21 cm
Therefore, the maximum height that the rabbit can reach during its jump is 6.21 cm.
To find the total length of the rabbit's jump, we need to find the x-intercepts of the function, which represent the points where the rabbit lands back on the ground. These are given by:
-0.296x^2 + 2.7x = 0
x(-0.296x + 2.7) = 0
x = 0, x ≈ 9.12
Therefore, the total length of the rabbit's jump is approximately 9.12 cm.
So, the correct response is: 6.2 cm high; 9.1 cm long.