a ball is thrown upward. its height ( h, in feet ) is modeled by the function h = -16t^2 + 64t+3, where t is the length of time ( in seconds ) that the ball has been in the air. what is the maximum height the ball reaches? a ball is thrown upward. its height ( h, in feet ) is modeled by the function h = -16t^2 + 64t+3, where t is the length of time ( in seconds ) that the ball has been in the air. what is the maximum height the ball reaches? @Mathematics

Question

mathmathmath · Answer

Find the critical point of the equation by taking the derivative and setting it equal to zero.

anonymous · Answer

how do i do that?

mathmathmath · Answer

You can use the power rule to find the derivative of each of the three parts to "-16t^2 + 64t+3"

amistre64 · Answer

-b/2a

amistre64 · Answer

given a quadratic in the form: ax^2 + bx + c

the axis of symmetry is the highest/lowest point.  And that is given by -b/2a

amistre64 · Answer

well, the axis of symm contains the high/low ....

mathmathmath · Answer

the derivative to -16t^2 + 64t+3 --> -32t+64. set this equal to zero to solve for the critical point.

amistre64 · Answer

the derivative method is fine, if you understand calculus ...

amistre64 · Answer

you still end up with 64/32

mathmathmath · Answer

-32t +64 = 0 --> -32t = -64 --> t=2

now solve for h(2), which means, solve the equation of height for the time value of 2

amistre64 · Answer

i forgot to finish reading it lol

mathmathmath · Answer

=]

anonymous · Answer

how do i find h?

mathmathmath · Answer

find h by plugging in the time value of 2....plug in t=2

anonymous · Answer

oh, ok so -16(2)^2+64(2)+3.  this is 1024+128+ 3. so the answer is 1155?

anonymous · Answer

the answer for h i mean

mathmathmath · Answer

assuming your algebra is correct, yes. But do you understand the process of solving for t?

anonymous · Answer

not really

mathmathmath · Answer

are you in a calculus class?

anonymous · Answer

no, algebra 2

mathmathmath · Answer

then I believe you're expected to solve it amistre64's way...sorry, I was speaking in calculus terms

anonymous · Answer

oh, well were going to go over it in class anyway. i just need the answers to get a grade. ill see how to solve it then

mathmathmath · Answer

well then you got your answer :P

anonymous · Answer

thanks for the help