Answer:
A: 46 meters at 3 seconds
B: 0 meters at 6.033 seconds
C. It depends where the tree is
D. 6.033 seconds
Step-by-step explanation:
A. To find max height, we need to find the vertex.
We can do this by using vertex from y=a(x-h)+k for y=a^2+b^2+c^2
h(t) = -5t^2+30t+1
h(t)+45 = - 5x^2+30x+45+1
h(t)+45= -5(x^2-6x-9)+1
h(t)+45 = -5(x-3)^2+1
h(t) = -5(x-3)^2+46
Hence, the max height is 46 at 3 seconds
B. The minimum height is 0 meters because of the problem
C. It depends because the parabola intersects x=10 in 2 places meaning that you need the tree to be in either of these two places to intercept the horseshoe
D. -5x^2+30x+1=0
5x^2-30x-1=0
x= (30+-sqrt(30^2-4*5*-1))/2*5
x=(30+-sqrt920)/10
x=3+-2sqrt230/10
x=3+-sqrt230/5
This means that x = -0.033 or 6.033. Negative value doesn't make sense so it's 6.033 seconds
