Find the rule for the quadratic. The h =24ft. The pumpkin retuerns to the ground after 6 seconds. Hint: wat is the height when it hits the ground? Use h +vt-16t^2
To find the rule for the quadratic equation, we need to use the given information and model the height of the pumpkin as a function of time.
We can start with the formula: h = vt - 16t^2, where h is the height, v is the initial velocity, and t is the time.
Given that the pumpkin returns to the ground after 6 seconds (t = 6), we can substitute this value into the equation:
h = v(6) - 16(6^2)
h = 6v - 576
Now, we also have the additional information that the height when it hits the ground (h) is 24 feet. By substituting this value in the equation, we can solve for v:
24 = 6v - 576
6v = 600
v = 100
Now we can rewrite the equation with the known values:
h = 100t - 16t^2
So the rule for the quadratic equation, representing the height of the pumpkin as a function of time, is h = 100t - 16t^2.