You may also like

problem icon

Parabolic Patterns

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

problem icon

Cubics

Knowing two of the equations find the equations of the 12 graphs of cubic functions making this pattern.

problem icon

Steady Free Fall

Can you adjust the curve so the bead drops with near constant vertical velocity?

Weekly Problem 48 - 2012

Stage: 4 Challenge Level: Challenge Level:1


$x^{2} - 6x + 11 = (x - 3)^{2} + 2$.

When the curve is rotated $180^\circ$ about the origin, the equation of the new curve will be
$y = -(x + 3)^{2} - 2$
   $= -x^{2} - 6x - 9 - 2$
   $= -x^{2} - 6x - 11$.


Note: the image of point $(a,b)$ under a $180^\circ$ rotation about the origin is the point $(-a,-b)$. An alternative method, therefore, is to replace $x$ and $y$ in the original equation by $-x$ and $-y$ respectively.




This problem is taken from the UKMT Mathematical Challenges.

View the previous week's solution
View the current weekly problem
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Copyright © 1997 - 2012. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.