The height y in feet of a ball thrown by a child is modeled by $y = - 0.1 x ^ { 2 } + 2.5 x + 5$ , 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

Question

Quizplus · Accepted Answer

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 $x = - \frac { b } { 2 a }$, 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.

The Height Y in Feet of a Ball Thrown by a Child