Solving quadratic equations AFDA U4_7 Solving quadratic equations

Solving quadratic equations is based on factoring quadratic expressions Background knowledge

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

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 }

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

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

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