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Based on the posted comments, I made the following changes: Manipulate[(*Define the quadratic function*)f[y_] := a y^2 + b y + c; (*Plot the quadratic function*) ParametricPlot[{f[y], y}, {y, -10, …

I would like some help to make the opening (concavity) of the parabolas go to the right or left, and not up or down. Manipulate[ Plot[a (y - k)^2 + h, {y, -10, 10}, PlotRange -> {{-10, 10}, {-10, …

I made some adjustments to the coordinates. Manipulate[With[{np = NextPrime[xf]}, Plot[{x^2}, {x, -10, xf}, Axes -> {True, True}, Epilog -> { Opacity[0.4], Purple, Line /@ Flatten[ Outer[List, Tabl …

I'm trying a version of the code with the concavity of the parabola upwards (y=x^2), but I'm not succeeding. I appreciate any help. Manipulate[ With[{np = NextPrime[xf]}, Plot[{Sqrt[x], -Sqrt[x]}, …

To test the parabolic sieve, my intention was for the graph to show the coordinates of two points on the parabola and the value of the intersection on the y-axis. A table with this information would a …

The code below is an attempt to obtain the graph of a parabola from two pieces of information: a focus and a directrix. I am not able to get the correct graphical shape of the parabola. I appreciate a …

According to taxicab geometry, there are 1226 possible paths from A(2,5) to B(7,9), all with a distance of 9 units, |2-7|+|9-5|=9. I wanted to write a code where I could be obtaining the plots of some …

I would like some help solving the following problem using Mathematica: Show that, no matter what the initial area of an equilateral triangle is, the sequence of areas (painted in black) of the figure …

dyb[n_] := Module[{i = 0}, If[n > 2 && PrimeQ[n], While[! PrimeQ[n + 2^i], i = i + 1;]; i]] primes = Select[Range[2, 97], PrimeQ]; resp = Table[dyb[n], {n, primes}]; Grid[Transpose[{primes, resp}], …

Given a prime number p, is there always a smaller positive integer exponent k such that p+2^k is also prime? We will call the smallest possible value of this exponent the k*. We could interpret this n …