This week in Pre-calculus 11 we learned a number of different ways to solve quadratic equations. One method that I liked was the quadratic formula. The quadratic formula can be used to solve any equation (rational, irrational, etc.), even ones involving fractions!

The quadratic formula is based off of the values in a general quadratic equation:

• 
• In this equation a is not equal to zero, a≠0

The quadratic formula:

Example:

1. Since the equation is set up in the pattern that we need it in we can find the values of a, b, and c. (a=2, b=-10, c=12)
2. since we have the values for a, b and c we can input them into the formula. (the two negatives in front of the 10 cancel each other out and make it a positive). 
3. After writing in the values you need to use BEDMAS to simplify the radicand in the numerator.
4. You then need to check if you can simplify the radical. We know that four is a perfect square, so we can write it as a whole number ().
5. after simplifying the radical you check to see if any of the coefficients have anything in common so that we can simplify the fraction. In this case all of the coefficients are divisible by 2.
6. Since our answer can’t be further simplified we leave it as is.

Example:

1. Since our equation isn’t written in the proper format we need to rearrange it. We do this by moving the 5 over to the left side.
2. Now that it is written in the proper format we can find the values of a, b and c. (a=1, b=3, c=-5).
3. Next you need to input what you know into the formula.
4. Simplify the radical using BEDMAS.
5.  Check to see if the radical can be simplified. can’t be written as a mixed radical.
6. Check if the coefficients have a common factor. (-3, 1, and 2 have nothing in common).
7. Since we can’t further simplify the answer we just leave it as is.