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
To find the maximum height that the rabbit can reach during its jump, we need to find the vertex of the parabola represented by the function.
The vertex of a parabola in the form y = ax^2 + bx + c is given by the formula:
x = -b/2a
In this case, a = -0.296 and b = 0.
Plugging in these values, we get:
x = -0/2(-0.296)
x = 0
To find the corresponding y-value (the maximum height), we substitute this value of x back into the original equation:
y = -0.296(0)^2 + 2.7
y = 2.7
Therefore, the maximum height that the rabbit can reach during its jump is 2.7 cm.
To find the total length of the rabbit's jump, we need to find the x-values where the parabola intersects the x-axis, which represent the points where the rabbit reaches the ground.
To find these x-values, we set y = 0 and solve for x in the equation:
0 = -0.296x^2 + 2.7
This quadratic equation can be solved by factoring or using the quadratic formula, but in this case, we will use factoring.
Factoring the equation, we get:
0.296x^2 = 2.7
x^2 = 2.7/0.296
x^2 = 9.1216
x = ±√9.1216
x = ±3.02
Since the rabbit cannot jump a negative distance, we take the positive value of x.
Therefore, the rabbit reaches the ground at x = 3.02 cm.
So, the total length of the rabbit's jump is 2 times the x-value where it reaches the ground:
2 * 3.02 = 6.04 cm
Therefore, the correct answer is:
• 2.7 cm high; 6.2 cm long