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


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


Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020