Understanding what you're doing.

  • Context: Undergrad 
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Discussion Overview

The discussion centers on the importance of understanding mathematical concepts and rules, particularly in the context of applying them to problems in engineering and mathematics. Participants explore the implications of comprehension versus rote application of mathematical techniques.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses concern about their understanding of mathematical rules and its potential impact on future performance in engineering courses.
  • Another participant emphasizes the importance of understanding math when facing new problems, suggesting that a solid foundation allows for better problem-solving approaches.
  • Several participants request clarification on the derivation of the formula h = -b/2a in quadratic functions, indicating a need for deeper understanding of the concept.
  • A participant explains that the axis of symmetry of a parabola can be derived from the roots of the function using Viete's formulas, leading to the conclusion that h = -b/2a.
  • Another participant mentions that the value of 'h' can be difficult to see in the general form of the quadratic expression but can be obtained through completing the square.
  • One participant asserts that understanding concepts is always helpful.

Areas of Agreement / Disagreement

Participants generally agree on the importance of understanding mathematical concepts, but there is a lack of consensus on the specific derivation of the formula h = -b/2a, with multiple explanations and approaches presented.

Contextual Notes

Some participants rely on different mathematical techniques and interpretations, such as Viete's formulas and completing the square, which may lead to varying levels of clarity regarding the concept of h in quadratic functions.

streetmeat
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How important is it to you to understand the math your applying? I am decent at math when it comes to remembering rules and applying everything systematically, and i do well at solving problems using the tools i am given, but sometimes i have trouble understanding exactly why certain rules work down to a science, which kind of bothers me and makes me worry about it affecting my performance later on if i take like an engineering course with intense math.
 
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It's important when you are confronted to a new sort of problem. Understanding the math you are applying allows you to know if what you know can be applied to that problem. From the foundations of your understanding, you will be able to attack the problem from the right angle.
 
it is extremely important
 
can someone please explain to me then why h = -b/2a in a quadratic function where f(x) = ax^2 + bx +c = a(x-h)^2 + k
 
streetmeat said:
can someone please explain to me then why h = -b/2a in a quadratic function where f(x) = ax^2 + bx +c = a(x-h)^2 + k

Huh? That's a bit of a weird change of topic! Expand the brackets and see what you get.
 
streetmeat said:
can someone please explain to me then why h = -b/2a in a quadratic function where f(x) = ax^2 + bx +c = a(x-h)^2 + k

Okay, say the parabola,
f(x)=ax^2+bx+c

Intersects the x-axis at points (a,b) and (c,d).

Show the axis of symettry is right in the middle of those two points on the x-axis. Meaning, (a+c)/2

But, "a" and "c" are the two roots (zeros) of f(x). And by Viete's formula the sum of the two roots is (-b/a). So h=(-b/a)/2 = (-b/2a)
 
streetmeat said:
can someone please explain to me then why h = -b/2a in a quadratic function where f(x) = ax^2 + bx +c = a(x-h)^2 + k
'h' is the value representing horizontal translation. The value is difficult (or impossible - depending on what/how much one knows) to see in general form of the expression; but by completion of the square, and then setting into standard form, you can obtain the value of 'h' directly.
 
Yes, always helpful to understand the concept.
 
Last edited:

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