4.4a Quadratic formula
Determine the roots of ax2 + bx + c = 0 by completing the square.
Yes, we have a fourth (and final) way to solve quadratic equations.
The quadratic formula (derived from completing the square) is used
when a quadratic expression is not factorable, meaning the roots are
irrational.
1.
2.
3.
4.
Graphing
Factoring
Completing the Square
Quadratic Formula
x=
-b ±√ b2 - 4ac
2a
Ex. Solve using the quadratic formula
a) 3x2 + 5x - 2 = 0
b) 4x2 + 5x - 1 = 0
Ch4 Quadratic Equations Page 1
c) 3x2 - 2x - 4 = 0
Ex. A field is to be fenced on three sides with a stream on the fourth side.
If there is 20 m of fencing and the field has an area of 42 m 2, what are
the dimensions of the field?
Assignment p254 #3acef,4acef,5acef,8,13a,14,12*
Ch4 Quadratic Equations Page 2