The height y in feet of a ball thrown by a child is modeled by $y=-0.1x^2+2.5x+5$ , where x is the horizontal distance in feet from where the ball is thrown. What is the maximum height of the ball? Round your answer to the nearest integer.

A) 7 feet
B) 11 feet
C) 21 feet
D) 35 feet
E) 52 feet

To find the maximum height of the ball, we need to find the vertex of the parabola. The x-coordinate of the vertex can be found using the formula $x=-\frac{b}{2a}$ , where a and b are the coefficients of the x terms in the equation. Plugging in the values, we get $x=-\frac{2.5}{-0.2}=12.5$ . To find the corresponding y-coordinate, we plug in x = 12.5 into the equation and get $y=-0.1(12.5{)}^2+2.5(12.5)+5=21.25$ . Rounded to the nearest integer, the maximum height of the ball is 21 feet, so the answer is C.