2.3 "Quadratic Equations"
If pq = 0 , what do we know?
Solve by factoring.
(ex) 3x2 = x +14
(ex) 2x2 ­ 3x = 20
Special Quadratic Equation
If x2 = d , then (ex) x2 = 16
(ex) x2 = 7
(ex) (x + 2)2 = 11
(ex) (x ­ 5)2 = 15
Completing the Square
(1)
(ex) x2 + 6x
or
(2)
(ex) x2 ­ 5x (ex) Determine the value of d that completes the square.
(b) x2 + dx + 25
(a) x2 + 13x + d
Solving a quadratic by completing the square.
(ex) x2 + 10x + 12 = 0
(ex) x2 ­ 12x ­ 15 = 0
(ex) 4x2 + 16x + 9 = 0
(ex) 9x2 + 18x ­ 1 = 0
.
Quadratic Formula
ax2 + bx + c = 0
(Let's complete the square on this general form of a quadratic)
Solve using the quadratic formula.
(ex) 5x2 + 13x = 6
.
(ex) 3x2 + 5x + 1 = 0