Question 33150
y=-0.005x^2+x+5 is a quadratic function representing parabola opening downward.
The maximum height is reached at its vertex; Hence the y-coordinate of the vertex will give us the required maximum height the ball can attain. 
If there is an x-intercept of a vertex, the larger x-intercept will give us the the distance the ball would travel horizontally when it hits the ground;
- I am providing the above explanation so that you will not only be able to solve this type of problems, but also be able to develop a concept behind this-......
x-coordinate of the vertex is attained at -b/2a (for function ax^2+bx+c);
Here, a=-.005; b=1; Hence x-coordinate of vertex = -1/(2)(-.005) = 1/.01 = 100;
y-coordinate of the vertex is f(-b/2a)
= f(100) = -.005(10^4) + 100 + 5 = -50+105 = 55;
Answer (1): Maximum height the ball can attain is 55 feet;
.........
x-intercepts are found by equating f(x) = 0;
So, -0.005x^2+x+5 = 0
=> .005x^2-x-5 = 0
=> 5x^2-1000x-5000 = 0
=> x^2-200x-1000 = 0
=> larger x= {-(-200) + Sqrt[(-200)^2-4(1)(-1000)]]/2(1) = [200+sqrt(44000)]/2
= 100+55sqrt(10);
Answer (2): The distance the ball would travel horizontally when it hits the ground is 100+55*sqrt(10) feet.