Welcome to our community

Be a part of something great, join today!

Problem Of The Week #406 Feb 27th, 2020

Status
Not open for further replies.
  • Thread starter
  • Admin
  • #1

anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,894
Here is this week's POTW:

-----

The parabola with equation $y=ax^2+bx+c$ and vertex $(h, k)$ is reflected about the line $y=k$. This results in the parabola with equation $y=dx^2+ex+f$. Find $a+b+c+d+e+f$.

-----

Remember to read the POTW submission guidelines to find out how to submit your answers!
 
  • Thread starter
  • Admin
  • #2

anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,894
Congratulations to the following members for their correct solution!

1. castor28
2. MegaMoh

Solution from castor28 :
If the generic point of the reflected parabola is $(x,z)$, we have $y+z=2k$. This gives:
$$
y+z = (ax^2+bx+c) + (dx^2+ex+f) = 2k
$$
for all $x$. Taking $x=1$ gives:
$$
a+b+c+d+e+f = 2k
$$
 
Status
Not open for further replies.