Skip to main content
Links to the University of Cambridge website
Links to the NRICH website Home page
Advent Calendars 2023
Or search by topic
Number and algebra
The Number System and Place Value
Calculations and Numerical Methods
Fractions, Decimals, Percentages, Ratio and Proportion
Properties of Numbers
Patterns, Sequences and Structure
Algebraic expressions, equations and formulae
Coordinates, Functions and Graphs
Geometry and measure
Angles, Polygons, and Geometrical Proof
3D Geometry, Shape and Space
Measuring and calculating with units
Transformations and constructions
Pythagoras and Trigonometry
Vectors and Matrices
Probability and statistics
Handling, Processing and Representing Data
Developing positive attitudes
For younger learners
Early Years Foundation Stage
Decision Mathematics and Combinatorics
Advanced Probability and Statistics
16 to 18
$X(r)$ is defined implicitly by the quadratic relationship
Which of the choices $r=1,-1,100$ give real values for $X(r)$?
What is the range of values of $r$ for which $X(r)$ takes real values?
What happens when $r=0$?
Sketch the overall shape of $X(r)$ against $r$ and find the maximum and minimum values of $X(r)$.
Note: You could numerically find a sensible conjecture for the minimum and maximum values of $X(r)$, but to prove this you will need to use calculus.
You may also like
Can you find a quadratic equation which passes close to these points?