Functions and Graphs Stage 4 - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Functions and Graphs - Stage 4.

Quadratic Rotation

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 48 - 2012
The curve $y=x^2−6x+11$ is rotated through $180^\circ$ about the origin. What is the equation of the new curve?

Unequal Statements

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

Weekly Problem 32 - 2010
For what numbers are each of these statements true? How many of the statements can be true at the same time?