**Name: __________________________________ QUADRATIC FORMULA**

The Quadratic Formula returns 2, 1 or no values by adding and subtracting the square root of the discriminant (the value under the radical).

__LAW OF TRICHTOMY__

A quantity must be one of three things:

- Less than zero (negative)
- Equal to zero
- Greater than zero (positive)

__DISCRIMINANT__

The value under the radical is the discriminant. Since you have to find the square root for
both equations, it is easier to do this first.

b^2 – 4ac

Using the Law of Trichtomy will tell you how many answers you have.

1. None because you cannot find the square root of a negative number.

2. Equal to zero one answer because you drop the plus or minus operations.

3. Greater than zero, you have to find the square root.

:
If not a perfect square, factor out perfect
squares and leave as a radical.

__THE
QUADRATIC____ FORMULA__

Given the form Ax^2 + Bx + c = 0 where

·
a is the coefficient of x^2

·
b is the coefficient of x

·
c is the constant

X1
= ( -b +** **sqrt ( b^2 – 4ac)) / 2a

X2
= ( -b **–** sqrt ( b^2 – 4ac)) / 2a

__PRACTICE__

Ø
Practice the Quadratic Formula to solve p. 380,
problems 23 – 28.

Ø Practice the Quadratic Formula with any other functions you cannot factor from the worksheet or problems 5 – 22. This helps you see how the formula works.

1. Factor out any common monomial first to make the problem easier.

2. List the values for a, b and c.

: Remember the sign in front of the coefficient stays with the number.

3. Find the value of the discriminant by substituting the values for a, b and c

4. Using the value of the discriminant substitute the values for a, b and c into the 2 functions.

4. Simplify the expressions

5. Check your answer(s) in the original equation.

__Examples: Record here and on the back!__