Desmos Calculator Mastery • Lesson 7 of 7

Equation Solving

Read the solutions of any equation straight off the x-axis.

To solve an equation, move everything to one side so it reads … = 0, graph y = that expression, and the x-intercepts are the solutions. For x^2 - 5x + 6 = 0, the curve crosses at x = 2 and x = 3. This handles quadratics, higher polynomials and ugly decimals that would be slow by hand.

  1. Rewrite the equation as (something) = 0.For example x^2 = 5x - 6 becomes x^2 - 5x + 6 = 0.
  2. Graph y = x^2 - 5x + 6.A parabola dips below the x-axis between its roots.
  3. Turn on key points and read the crossings.x = 2 and x = 3 are the solutions.

If the curve never touches the x-axis, the equation has no real solution. If it just touches at one point, there is exactly one (a repeated root).

Try it liveSolve a quadratic graphically
  • y = x^2 - 5x + 6 is loaded.
  • Tick key points to see the roots x = 2 and x = 3.
  • Try y = x^2 + 1 — it never crosses the axis, so no real solution.
← Intersection Finding Try a full-length mock →