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SOLVING QUADRATIC EQUATIONS IN THE THREE FORMS

Finding the x/y-intercepts and the Vertex

Vertex Form

  1. First you should find your vertex and you can easily identify through this form as they are "h" and "k". 

  2. Find the y-intercept, to do so, substitute "x" with zero and solve through "BEDMAS"

  3. Find the x-intercept by substituding "y" with zero and solving through "reverse bedmas" (You may recieve zero/one/two answers as after square rooting the answer). "If the number you are square rooting is a negative, it means that your graph will have no x-intercepts.

  4. Graph the intercepts and vertex

Factor Form

  1. Since its a factor form, you know the x intercepts, the signs of the numbers just have to be switched. 

  2. Add the two roots together and divide them to get your (Axis of Symmetry)

  3. Sustitude your axis of symmetry back into your original equation and evaluate to recieve your optimal value and finalize your vertex

  4. Graph the intercepts and vertex

Standard Form

  1. Use the quadratic formula, take your three values from "a", "b", and "c" and substitute into the quadratic formula, or you can use another method which is factoring the equation into factored form. (either way, the steps are still the same and don't change which ever choice you make).

  2. Evaluate them to recieve your zero/one/two x- intercepts. Then switch the signs of the x-intercepts and follow the steps done in FACTORED FORM.

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