Understanding the Point-to-Point Equation in a Book

  • Thread starter Thread starter giant016
  • Start date Start date
  • Tags Tags
    Book
Click For Summary
SUMMARY

The discussion focuses on the application of the point-to-point equation as presented in a specific book. The user clarifies the transition from the equation area = height × width to the expression [-(2i/5)² + 5](2/5) by substituting x = 2i/5 into the function f(x) = -x² + 5. This substitution is crucial for understanding how to derive the height from the given function. The user acknowledges the importance of recognizing the quadratic function in the context of the problem.

PREREQUISITES
  • Understanding of quadratic functions, specifically f(x) = -x² + 5
  • Familiarity with substitution methods in algebra
  • Basic knowledge of area calculations in geometry
  • Ability to manipulate complex expressions involving variables
NEXT STEPS
  • Study the properties of quadratic functions and their graphs
  • Learn about substitution techniques in algebraic expressions
  • Explore applications of area calculations in various mathematical contexts
  • Investigate the implications of point-to-point equations in physics or engineering
USEFUL FOR

Students studying algebra, educators teaching quadratic functions, and anyone interested in the application of mathematical equations in real-world scenarios.

giant016
Messages
20
Reaction score
0

Homework Statement


Sigma.jpg

I'm just having trouble seeing how the book is getting from point-to-point. I understand the area=height X Width part of the equation, but I don't see how in the seconds step (2i/5)(2/5) turns into [-(2i/5)^2+5](2/5). Smae goes for the second step in the second equation circled in red.
 
Physics news on Phys.org
height is given by f(x) = f(2i/5) so you plug in x=2i/5:
[tex]f\left(\frac{2i}{5}\right)=-\left(\frac{2i}{5}\right)^2+5[/tex]

same goes for the second equation

you have an expression for x as a function of i that you plug into find f as a function of i.
 
Ahh, now I see. I totally forgot about the f(x)=-x^2 equation. Thanks!
 

Similar threads

  • · Replies 21 ·
Replies
21
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 14 ·
Replies
14
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
2
Views
2K