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:
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
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!