A ball is thrown upward and outward from a height of 77 feet. the height of the ball, f(x), in feet, can be modeled by f left parenthesis x right parenthesis equals negative 0.2 x squared plus 1.4 x plus 7f(x)=−0.2x2+1.4x+7 where x is the ball's horizontal distance, in feet, from where it was thrown. use this model to solve parts (a) through (c).
From the given function modeling the height of the ball: f(x)=-0.2x^2+1.4x+7 A] The maximum height of the ball will be given by: At max height f'(x)=0 from f(x), f'(x)=-0.4x+1.4 solving for x we get: -0.4x=-1.4 x=3.5ft thus the maximum height would be: f(3.5)=-0.2(3.5)^2+1.4(3.5)+7 f(3.5)=9.45 ft
b] How far from where the ball was thrown did this occur: from (a), we see that at maximum height f'(x)=0 f'(x)=-0.4x+1.4 solving for x we get: -0.4x=-1.4 x=3.5ft This implies that it occurred 3.5 ft from where the ball was thrown.
c] How far does the ball travel horizontally? f(x)=-0.2x^2+1.4x+7 evaluationg the expression when f(x)=0 we get: 0=-0.2x^2+1.4x+7 Using quadratic equation formula: x=-3.37386 or x=10.3739 We leave out the negative and take the positive answer. Hence the answer 10.3739 ft horizontally.
