The function y = -0.296x^2 + 2.7× 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)
• 2.7 cm high; 0.296 cm long
• 6.2 cm high; 9.1 cm long
• 4.6 cm high; 6.2 cm long
• 9.1 cm high; 6.2 cm long
choose one of the answer choices
To find the maximum height that the rabbit can reach during its jump, we need to determine the vertex of the parabola represented by the given function.
The given function is in the form of y = ax^2 + bx. The x-coordinate of the vertex can be found using the formula x = -b/2a.
For this function, a = -0.296 and b = 2.7. Plugging these values into the formula, we get x = -2.7/(2*(-0.296)) = 4.563.
To find the corresponding y-coordinate of the vertex, we substitute this value of x back into the function: y = -0.296(4.563)^2 + 2.7*4.563 = 6.236.
Therefore, the maximum height that the rabbit can reach during its jump is approximately 6.2 cm.
To find the total length of the rabbit's jump, we need to find the x-intercepts (where y = 0) of the parabola.
Setting y = 0 in the given function, we get:
0 = -0.296x^2 + 2.7x
0 = x(-0.296x + 2.7)
Solving for x, we find x = 0 (which implies the starting point or ground) and x = 2.7/0.296 = 9.13 (rounded to two decimal places).
Therefore, the total length of the rabbit's jump is approximately 9.1 cm.
The answer is: 6.2 cm high; 9.1 cm long.