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Quadratic Equations

Recall that a linear equation in one variable is of the form ax+b=0 , where a and b are constants and a0 .

For example:

3x+5=0 6x2=0

A quadratic equation has an x 2 ( x -squared) term. ("Quadratum" is Latin for square.)

The general quadratic equation in standard form looks like

a x 2 +bx+c=0 , . . . . where a0 .

If we want to find the x or x 's that work, we might guess and substitute and hope we get lucky, or we might try one of these four methods:

  • Guess and Check
  • Solving by Square Roots (if b=0 )
  • Factoring
  • Completing the Square
  • The Quadratic Formula
  • We can solve graphically by equating the polynomial to y instead of to 0 , we get an equation whose graph is a parabola. The x -intercepts of the parabola (if any) correspond to the solutions of the original quadratic equation.

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