The maximum height that the rabbit can reach during its jump is found at the vertex of the quadratic function. We can find the x-coordinate of the vertex by using the formula x = -b / (2a), where a and b are the coefficients of the quadratic function in the form ax^2 + bx + c.
In this case, a = -0.296 and b = 2.7. Plugging these values into the formula, we get x = -2.7 / (2(-0.296)) = -2.7 / (-0.592) = 4.569
To find the y-coordinate of the vertex (or the maximum height), we can substitute this value of x back into the function:
y = -0.296(4.569)^2 + 2.7(4.569) ≈ 6.2
So, the maximum height that the rabbit can reach during its jump is approximately 6.2 cm.
Once the rabbit reaches the ground, its height y is 0. So, we set y = 0 and solve for x to find the x-coordinate of the other point where the function crosses the x-axis (the ground):
0 = -0.296x^2 + 2.7x
We can factor out an x from both terms:
x(-0.296x + 2.7) = 0
Either x = 0 or -0.296x + 2.7 = 0
Solving -0.296x + 2.7 = 0, we get x = 2.7 / 0.296 ≈ 9.1
So, the rabbit jumps approximately 9.1 cm.
Therefore, the answer is B. 6.2 cm high; 9.1 cm long.
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?
A. 2.7 cm high; 0.296 cm long
B. 6.2 cm high; 9.1 cm long
C. 4.6 cm high; 6.2 cm long
D. 9.1 cm high; 6.2 cm long
1 answer
1 answer