1. Solving quadratic equations
AFDA U4_7
Solving quadratic equations

2. Solving quadratic equations is based on factoring quadratic expressions
Background knowledge

3. Steps to solving a quadratic equation
1. Set the expression equal to zero
2. Factor it
3. Set each binomial equal to zero
4. Solve for the unknown

4. solving a quadratic equation
x2 + 7x + 6
Set the expression equal to zero
x2 + 7x + 6 = 0
Factor it
(x + 6)(x + 1)
Set each binomial equal to zero
x + 6 = 0 x + 1 = 0
Solve for the unknown
x = – 6 ; x = –1
x= {– 1, –6 }

5. solving a quadratic equation
When we solve a quadratic, we are finding the zeros or roots

6. solving a quadratic equation
Expressions have Factors; Equations have Roots (Zeros)

7. Deriving an equation from its roots
Derive an equation that has zeros at 5 and –4
Set up two sets of parentheses
( )( )
Put an x in the left hand part of each set parentheses
( x )(x )
Put the roots (zeros) in the right hand part of each set of parentheses WITH THE OPPOSITE SIGN
( x – 5)(x + 4)
Multiply the two binomials
x2 – x – 20
Set y equal to the product of the two binomials
y = x2 – x – 20