Present the definition of a quadratic equation. Stress to students that the equation must contain a term with a variable squared, but the other terms do not need to contain a squared variable.
Tell students to set the equation equal to zero and explain the typical format of a quadratic equation (ax^2 + bx + c = 0).
Tell students to factor the quadratic equation. Start with equations in which a = 1, as these are the simplest to factor by hand. In these cases, students should look for two numbers with a product of c and a sum of b. For example, if the equation is x^2 + 3x + 2 = 0, the factored form would be (x + 1)(x + 2) = 0.
Instruct students to solve for x in each factor individually so that factor is equal to zero. Explain that most quadratic equations have two unique solutions. For equations in which a = 1, solving for x is simply a matter of changing the sign of the number in that factor. Using the previous example of (x + 1)(x + 2) = 0, you would get x = -1 and x = -2.
Have students factor quadratics in which the first coefficient is not equal to one, after students master the ability to factor simple quadratic equations by hand.
Present the quadratic formula, which is useful for solving quadratics that are not easily factored by hand. The quadratic formula is: x = [-b +/- (b^2 - 4ac)^(1/2)]/2. The "+/-" sign means that one solution is obtained by using a "+" and the other solution is obtained by using a "-" in the formula. In addition, note that raising something to the 1/2 power is equivalent to taking its square root. Remind students that they do not need to change the sign of the output of the formula as they did when they factored equations by hand.
Graph a few sample quadratic equations on the board. Explain that "c" is the y-intercept of the graph and that larger values of "a" lead to steeper slopes of the parabola.