The function y= -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)
To find the maximum height, we need to identify the vertex of the parabola representing the function. The vertex is given by the formula x = -b / (2a), where a and b are the coefficients in the quadratic equation. In this case, a = -296 and b = 2.7.
x = -2.7 / (2 * -296)
x = -2.7 / -592
x ≈ 0.0046
Now let's substitute this value of x into the equation to find the maximum height.
y = -296(0.0046)^2 + 2.7(0.0046)
y ≈ -0.6 + 0.0124
y ≈ -0.5876
The maximum height that the rabbit can reach during its jump is approximately -0.5876 centimeters.
To find the total length of the rabbit's jump, we need to determine the two x-intercepts of the function, which represent the points where the parabola intersects the ground (y = 0).
-296x^2 + 2.7x = 0
Factoring out an x:
x(-296x + 2.7) = 0
Setting each factor equal to zero:
x = 0 or -296x + 2.7 = 0
Solving for x in the second equation:
-296x + 2.7 = 0
-296x = -2.7
x ≈ 0.0091
So the rabbit jumps a total length of approximately 0.0091 centimeters.
In conclusion, the maximum height the rabbit can reach during its jump is about -0.5876 centimeters, and the total length of the jump is approximately 0.0091 centimeters.