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


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


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