SOLUTION: I am doing "Applications of Quadratic Equations" and the textbook constantly asks 'What are the possible values for t, h whatever'. Eg. h=16t-4t^2 or h=-1/16(d-10)^2 + 9 I am try

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Question 610063: I am doing "Applications of Quadratic Equations" and the textbook constantly asks 'What are the possible values for t, h whatever'.
Eg. h=16t-4t^2 or h=-1/16(d-10)^2 + 9
I am trying to find the possible values for the pronumeral subsitituiting x.
I have tried the quadratic formula which gave me the correct solution for h=-1/16(d-10)^2 + 9 but not h=16t-4t^2.
How else can I solve this question without trial and error (which takes forever?)
THANKYOU!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
RANT:
The quadratic formula makes people believe that math is a question of memorizing formulas. Math is really a very easy foreign language. Once you remember the meaning and usage of a few symbols, you can use your brain to get all the rest. Unfortunately teachers worship memorization and start brainwashing you about it in the early grades. No one tries to memorize a list of the phone numbers of friends and relatives; they just start remembering them from use, after looking them up as needed. Why should anyone memorize the times tables?

SOLUTION:
h=16t-4t%5E2 --> h-16t=16t-4t%5E2-16t --> h-16t=-4t%5E2
h-16t=-4t%5E2 --> %28-1%2F4%29%28h-16t%29=%28-1%2F4%29%28-4t%5E2%29 --> -h%2F4%2B4t=t%5E2 --> t=sqrt%284t-h%2F4%29 or t=-sqrt%284t-h%2F4%29
I'll go faster with the other one (let me know if I made mistakes with either one).
h=-%281%2F16%29%28d-10%29%5E2+%2B+9 --> h-9=-%281%2F16%29%28d-10%29%5E2 --> 16%289-h%29=%28d-10%29%5E2
From there you get
d-10=sqrt%2816%289-h%29%29=4sqrt%289-h%29 or d-10=-4sqrt%289-h%29
and adding 10 to both sides, you get
d=10+%2B-+4sqrt%289-h%29
Who needs the quadratic formula?

NOTE 1:
What the textbook should be trying to explain is that quadratic equations are used to solve problems in physics, such as finding the height, h, of a moving object, after a downwards force started acting on it.
You may relate height, h, to time (t) or distance (d) by an equation like the ones given in your problem. After that, you may need to find t or d when the object is at a certain height, and then you would have to solve the equation for t or d.
If you need to do it for just one value of h, you could enter that value before solving. If your problem involves more than one value of h, or graphing as a function of h, then you need to solve the equation with the h in it, as done above.
(Of course, to math and/or physics snobs, you look much brighter if you always solve the equation with an h in it).

NOTE 2:
Sometimes you need to solve quadratic equations in chemistry too (I am a chemist), but not often.