Confusing Math Problem?!?

I've been having trouble with these kind of problems and my math teacher gave us some formulas with A, B, and C to find the maximum point, minimum point, and axis of symettry...or something like that! I'm so confused and I'm hoping that some math genius will help me undo this confusion!!!! =)


I've been having trouble with problems like this:





1. A baseball is hit so that its height in feet in t seconds after it is hit can be represented by: h(t)= -16t+56t+4


a) What is the height of the baseball when it is hit?


b) When does the baseball reach a height of 25 feet?


c) What is the baseball's maximum height?





Thank YOU so Much in ADVANCE =)


BTW...if you could provide those formulas for max point, min point, axis of symettry, etc...that would be appreciated =)

Confusing Math Problem?!?
For part a, when the baseball is hit, time is 0 since it is 0 seconds after it is hit, so set t = 0. So h(t) = -16*0 + 56*0 + 4, so 4 feet is the answer.





For part b, they are telling you h(t) is 25, so just plug that into the equation. 25 = -16t + 56t + 4. Just solve for t, I'm sure you can do that yourself. (Hint : Quadratic Formula)





For part c, I'm assuming you're not in calculus, so I won't do it using derivatives. To do it algebraically, you have to find the axis of symmetry. The formula for Axis of Symmetry is


x = -b/2a. This will give you the x-coordinate of the axis of symmetry. So the axis of symmetry in this case is


t = -56/(2*-16), which will give you t = 1.75. To find the maximum height, you want to find the y-coordinate that lies on the axis of symmetry. To do this, go back to your equation and plug in 1.75 for t. so h(t) = -16(1.75) + 56(1.75) + 4. You get a final answer of 53 feet.
Reply:I'm assuming thats -16t^2





Well, look: h(t) means that h is a function and t is one of its arguments. Therefore, whatever is in place of t in the parentheses, you replace t with that in the equation.





For example: h(3) = -16(3)^2 + 56(3) + 4





a)When the ball is hit, t = 0, so it's just h(0). The 1st two terms are gone, because they're both multiplied by 0, which is zero, so you're left with 4 feet





b)Now you have to substitute in 25 for h(t) and solve for t.


So you get 25 = -16t^2 + 56t + 4





Using quadratics, the other side of the equation must be 0, so subtracting 25 from both sides gives us:





-16t^2 + 56t - 21 = 0


now use the quadratic formula: t = (-56 (plus or minus) sqrt(56^2 - 4(-16)(-21)))/(2(-16))





so t has 2 solutions: 0.427 s, and 3.073 s





c)this involves the vertex of the parabola, whose x-coordinate on the graph can be found by -b/2a, or in this case -56/(2(-16)) = 7/4





now plug 7/4 in as t, so -16(7/4)^2 + 56(7/4) + 4, which equals 53 feet
Reply:a)When the ball is hit, t=0 so h(t)=h(0)=-16(0)+56(0)+4=4


so when the ball is hit its height is 4


b)h(t) represents the height of the ball after t seconds so the ball reaches 25 feet when h(t)=25 but if h(t)=25 that means -16t+56t+4=25


40t=21


t=21/40 (by the way r u sure that the question is about -16t+56t+4 and not -16t^2+56t+4 cause that would make more sense)


c)Here again i think that the question must be -16t^2+56t+4


but if it is as it is then the answer would be +infinity


by the way i am sry for the bad English
Reply:a] h=-16t+56t+4 (t=0)


h=-16(0)+56(0)+4


h=4 %26lt; height of baseball when hit


b] h=25 (sub in 25 for h and solve)


c] factor, average the zeros, sub in x as t for your equation and solve.