Question 1)
We want to know when y hits 0, since that's when it lands.
[tex]0 = -0.04x^{2} + 8.3x + 4.3[/tex]
When we factorise, we get x = 208.01679... and -0.51679...
We can disregard the latter, because we know that x > 0, for the horizontal distance. Thus, we get 208.02 metres as our horizontal distance (A)
Question 2)
Using the same method as above, we want to know when the rock hits the ground. Thus, we want to know when y = 0, meaning that it hits the ground.
[tex]-0.05x^{2} + 4.5x - 6.5 = 0[/tex]
You can use the quadratric equation to find that x = 88.5316... and 1.4684...
Thus, the answer must be 88.53 metres.
Question 3)
Since we're dealing with a quadratic, there should theoretically be 2 solutions. Let's use the discriminant to check how many solutions there are.
[tex]\delta = b^{2} - 4ac[/tex]
[tex]= 2^{2} - 4(5)(-12) > 0[/tex]
Since the discriminant is greater than zero, there lies two solutions.
