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Puzzles

23 December

I draw the parabola y=x2 and mark points on the parabola at x=17 and x=6. I then draw a straight line connecting these two points.
At which value of y does this line intercept the y-axis?

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6 December

p(x) is a quadratic with real coefficients. For all real numbers x,
x2+4x+14p(x)2x2+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,
x22x+2p(x)2x24x+3
p(11)=181. Find p(16).

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Parabola

On a graph of y=x2, 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?

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