mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

6 December

\(p(x)\) is a quadratic with real coefficients. For all real numbers \(x\),
$$x^2+4x+14\leq p(x)\leq 2x^2+8x+18$$
\(p(2)=34\). What is \(p(6)\)?

Between quadratics

Source: Luciano Rila (@DrTrapezio)
\(p(x)\) is a quadratic polynomial with real coefficients. For all real numbers \(x\),
$$x^2-2x+2\leq p(x)\leq 2x^2-4x+3$$
\(p(11)=181\). Find \(p(16)\).

Show answer

Parabola

On a graph of \(y=x^2\), two lines are drawn at \(x=a\) and \(x=-b\) (for \(a,b>0\). The points where these lines intersect the parabola are connected.
What is the y-coordinate of the point where this line intersects the y-axis?

Show answer & extension

Archive

Show me a random puzzle
 Most recent collections 

Tags

fractions arrows games trigonometry 2d shapes dodecagons multiples perimeter doubling integration people maths star numbers division perfect numbers crossnumbers integers surds clocks partitions factors folding tube maps differentiation means ellipses angles cards sum to infinity colouring irreducible numbers routes algebra probability triangles advent squares graphs calculus square roots functions coins time prime numbers square numbers shape regular shapes dates probabilty money hexagons polygons spheres cryptic crossnumbers taxicab geometry chocolate averages percentages symmetry parabolas quadratics geometry floors remainders indices menace crosswords digits planes palindromes balancing addition coordinates complex numbers factorials books cube numbers christmas scales volume area 3d shapes sport dice number wordplay logic cryptic clues triangle numbers lines grids numbers rectangles ave sequences pascal's triangle unit fractions chess mean proportion multiplication shapes bases speed odd numbers chalkdust crossnumber circles sums rugby

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2019