Solving Quadratic Equations to Help My Kid

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Discussion Overview

The discussion revolves around solving a quadratic equation, specifically the equation -125 = 39.1t - 4.9t^2, with the aim of helping a participant's child with homework. The conversation includes various methods for solving quadratic equations, such as the quadratic formula and graphing, and explores the implications of the solutions in a physics context.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty in solving the quadratic equation and seeks guidance on the steps involved.
  • Another participant suggests using the quadratic formula as a method to solve the equation.
  • It is noted that the equation may not have rational roots and cannot be factored in the usual way.
  • A participant mentions that they obtained a solution of approximately 10.4 using the quadratic formula, but acknowledges the presence of two potential solutions due to the +/- option in the formula.
  • There is a discussion about the relevance of negative solutions in the context of a physics problem, suggesting that only positive values may be applicable for time.
  • A suggestion is made to graph the quadratic equation to illustrate the solutions visually, emphasizing that both roots are valid solutions to the equation.
  • A participant reflects on their learning experience and expresses appreciation for the resources available for understanding the topic better.

Areas of Agreement / Disagreement

Participants generally agree on the use of the quadratic formula and the idea that both solutions are mathematically valid. However, there is a discussion about the applicability of negative solutions in the context of the problem, indicating a nuanced view on the relevance of each solution.

Contextual Notes

Some participants express uncertainty about the quadratic formula and its application, indicating a potential gap in prior knowledge. There is also a mention of technical issues with sharing graphical representations, which may limit the discussion's depth.

Who May Find This Useful

This discussion may be useful for parents assisting children with homework on quadratic equations, students learning about solving such equations, and individuals interested in the application of mathematics in physics problems.

AC5FFw
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While a problem, this is more for me to learn to help my kid with her own homework. I used to be great at this sort of thing but for some reason I just can't get my head around this one.

-125 = 39.1t - 4.9t^2

I need to find the value for t. It should be approx 10.4. I would just like to see the steps to get there.

I know that I should re-write this as : 4.9t^2 - 39.1t - 125 = 0 But after this I am stuck...

Thx!
 
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Are you familiar with the quadratic formula? That is how the problem is solved.

Thanks
Matt
 
Don't think so. Guess I could google it.
 
Check it out.

Thanks
Matt
 
Very few quadratic equations can be solved by "factoring". All can be solved by "completing the square" or the "quadratic formula". That doesn't look like it will have rational roots and so cannot be "factored" in the usual way.
 
Just reading on the quadratic equation now.
I don't think I was ever taught this. So, when I look at an equation like the one above I try to see how to simplify it further. WoW what Fun!
 
Plugged this formula into the quadratic equation and got my 10.4 as one of the results.

With the +/- option, I take it I have to figure out both then plug them back into the equation. One works and the other does not. So I know that "t" has to equal 10.4

Sound about right?
 
AC5FFw said:
Plugged this formula into the quadratic equation and got my 10.4 as one of the results.

With the +/- option, I take it I have to figure out both then plug them back into the equation. One works and the other does not. So I know that "t" has to equal 10.4

Sound about right?
For your equation, both of the values you found are solutions. Since your quadratic equation comes from what appears to be a physics problem, a negative value for t might not be applicable, since that would represent a time before the object was released.
 
To illustrate the fact that both values you get are solutions, you can use a graph. A quadratic equation such as the one you gave can be graphed. For example, you can rewrite your equation by putting all the terms on one side of the equal sign:

4.9 x^2 - 39.1 x - 125 = 0

Then, instead of having '0' on the right side of the equation, you can put in a dependent variable, 'y'. Now, solutions to your original equation are points on a graph where y=0, or what are called 'roots' of the equation. Due to the shape of such a graph, it is apparent that you frequently have *two* answers that work, like so:

27wxbh1.png


Where the red graph of your quadratic cross the black x-axis (where y is equal to zero), you have the solutions to your problem.
 
  • #10
Lumen...

Your graph/pic did not come up.. but that's more of a issue with my server here.. All sorts of restrictions. I will check this out when I get home this evening...

Thank you all! I'm definatly a lot smarter on this now than I was yesterday! LOL
Where were all these great helpful tools when I was in school! If I would have had the resources that are available now... I would have enjoyed my time in school a lot more, and probably would have gone much further in my education as well.. :)

Please.. don't say it... I know, it's "Never Too Late" :D
 

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