This week in Pre-Calculus 11 i learned a number of different things about quadratic formulas and graphing. One thing that really stuck with me was how to convert from the general form to standard form and so on. Knowing how to convert between the two formulas can help you find more information about a graph.

Example:

• Note: When going from the general form to the standard form, you need to use the difference of squares method [creates a set of zero pairs])
•  First what you would do is check and see if there is a coefficient in front of the , if there is a coefficient in front then you would need to get rid of it to make the question easier. To get rid of the coefficient all you would need to do is divide the first TWO terms by the coefficient. *Do not divide the third term by the coefficient*
• You would then put brackets around the first two terms and bring the coefficient of the first term in front.
• Next, you create the zero pairs and add them inside of the brackets. To do this you take the term in the second part of the bracket (bx, ie. 4x), divide it by two and then square it. You then write it inside the brackets using +/- to make it a zero pair. *The first three terms inside the brackets should  create a perfect square trinomial*
• Then next step is to get the 4th term in the brackets outside of the brackets and simplify the perfect square trinomial [write in format of: ]. All you need to do to get the 4th term out of the brackets is to multiply it by the coefficient that is in front of the brackets and add it to the number at the end of the equation.
• To change the format of the perfect square trinomial you take the third term and divide it by two, you then write it into the formula where the variable, p is. *make sure that the sign in between the x and p matches the one in the middle term of the perfect square trinomial*

Example:

• In order for you to change the standard form to the general form all you need to do is expand the equation.
• First, to make things easier, you would rewrite the equation so that the squared binomial is side by side and not written in a condensed form. After rewriting it out you multiply the brackets together.
• Next you add up all of the like terms, and your equation should be written in the general form.