This week in Pre-Calculus 11 we learned about discriminant’s and how they can be useful. A discriminant is a portion of the quadratic formula that you can use to predict how many solutions you will have, based on if the value is positive, negative, or equal to zero. When graphing the discriminant represents how many times that the parabola touches the x axis. You should also note that finding the discriminant is NOT a way of solving quadratic equations.

Note, if the value of the discriminant is:

• Positive: then that means that you will have to solutions
• Negative: then that means that there are no solutions
• Equal to zero: then that means that there is one solution

The formula for finding the discriminant:

*highlighted in yellow*

Example:

1. Firstly, since our equation is already written in the proper format of (), we need to write down the values for a, b, and c. (a = 2, b = 9, c = -4)
2. Next, we input our values into the formula.
3. Use BEDMAS to simplify the equation until you are left with a value.
4. Since the number we are left with is 113, and it is positive, then we know that this quadratic equation will have two possible solutions.

Example:

1. First we need to identify the values of a, b, and c. (a = 6, b = -2, c = 7)
2. Next we input the values that we know into the formula.
3. Use BEDMAS to simplify to a value.
4. Since the value that we are left with is 164, and it is negative, we know that that this quadratic equation will have no solutions.

Example:

1. Firstly, since our equation is not in the proper format we need to rearrange it so that it is.
2. Now that the equation is in the proper format we can write down the values for a, b, and c. (a = 1, b = -8, c = 16)
3. Input the values that you know into the formula.
4. Use BEDMAS to simplify to a value.
5. Since what we are left with is zero, we know that this quadratic formula will have one solution.