DDesmos SAT Prep
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Polynomial-to-Polynomial Intersections

Find every crossing point between two higher-degree curves at once.

The Desmos trick

Graph both polynomials in the same calculator and click every visible intersection point — curves of degree 2 or higher can cross more than twice, so zoom out first to make sure you've found all of them.

  • Graph both polynomials on separate lines
  • Zoom out before counting intersections — higher-degree curves can cross far from the origin
  • Click each crossing point individually to read its exact coordinates

Practice questions

Q1What are the points of intersection of y = x^2 and y = x + 2?
Medium
Q2At how many points do y = x^3 and y = x intersect?
Medium
Q3What is the sum of all x-coordinates where y = x^3 - 3x and y = x inte…
Hard
Q4Which of the following is a point of intersection of y = x^2 - 1 and y…
Hard
Q5The graphs of y = x^3 - 6x^2 + 9x and y = x intersect at three points.…
Hard