To find the maximum height that the rabbit can reach, we need to find the vertex of the parabola represented by the given equation. The vertex of a parabola in the form y = ax^2 + bx + c is given by the coordinates (-b/2a, f(-b/2a)).
In this case, a = -0.296 and b = 2.7.
Using the formula for the x-coordinate of the vertex, we get:
x = -b/2a = -2.7 / (2 * -0.296) ≈ 4.6
Plugging this value of x back into the equation, we can find the corresponding value of y (the height):
y = -0.296(4.6)^2 + 2.7(4.6) ≈ 6.2 cm
So, the maximum height that the rabbit can reach during its jump is 6.2 cm.
To find the total length of the jump, we need to find the x-intercepts of the parabola. These are the points where the equation y = 0.
Setting the equation -0.296x^2 + 2.7x = 0 and factoring out an x, we get:
x(-0.296x + 2.7) = 0
Solving for x, we get:
x = 0 or -0.296x + 2.7 = 0
x = 0 or -0.296x = -2.7
x = 0 or x ≈ 9.1
The total length of the jump is the distance between these two x-intercepts:
9.1 cm - 0 cm = 9.1 cm
Therefore, the correct answer is: 6.2 cm high; 9.1 cm long.
The function y equals negative 0.296 x squared plus 2.7 x 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
1 answer