MHB Erika's Equations | Math Solutions & Help

  • Thread starter Thread starter lolab
  • Start date Start date
AI Thread Summary
The discussion centers around solving a set of equations derived from a quadratic function, specifically addressing the impossibility of having two different outputs for the same input. The equations are based on points (1, 5) and (2, 10) on the graph of the function, leading to a contradiction when a third point (2, 19) is introduced. This contradiction arises because both equations for the value at x=2 yield the same left-hand side, making it impossible for them to equal different right-hand sides. The suggested approach involves solving the equations step-by-step, but the underlying issue of conflicting outputs remains a critical point of discussion. The conclusion emphasizes the impossibility of finding values for a, b, and c that satisfy the conflicting equations.
Mathematics news on Phys.org
Screen Shot 2022-06-15 at 2.05.00 PM.png
 
Do you understand how they got the first two equations? Can you get part a)?

As to the second part you have three equations in three unknowns. I'd solve the first equation for c, then plug that into the other two equations. Then solve one of them for b and plug that into the next. Then solve the last equation for a.

See what you can do with this and if you are still having problems post what you've got and we can take a look at it.

-Dan
 
This is immediately impossible. f(2) cannot have two different values!

We are given $y= f(x)= ax^2+ bx+ c$. The fact that (1, 5) is on its graph (a parabola) means that $y= 5= a(1)^2+ b(1)+ c= a+ b+ c$.
The fact that (2, 10) is on the graph means that $y= 10= a(2)^2+ b(2)+ c= 4a+ 2b+ c$.

If (2, 19) were also on the graph we would have $y= 19= a(2)^2+ b(2)+ c= 4a+ 2b+ c$.

So we have both $10= 4a+ 2b+ c$ and $19= 4a+ 2b+ c$.

What do you get if you subtract the first equation from the second? Is there ANY value of a, b, and c which will make that true?
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

B Attempt to solve this system of three linear equations
Replies
10
Views
2K
News Tropical Storm Erika (August 2015)
Replies
4
Views
1K
MHB Is this Trigonometric Expression a Constant Function of x?
Replies
2
Views
1K
MHB Find the area of the shaded region
Replies
2
Views
1K
MHB How to Convert Miles to Kilometers with a Conversion Chain
Replies
6
Views
1K
MHB Can You Find the Angle in This Isosceles Triangle Problem?
Replies
1
Views
1K
MHB Can the Partial Sum of a Difficult Series be Solved with Induction?
Replies
6
Views
2K
MathHelpBoards.com merges with PF
Replies
42
Views
5K
MHB Find the amount of sand in each bag
Replies
1
Views
1K
MHB Equation Logarithmic: Solve x | MHB Help
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top