Chapter 9: Quadratic Equations
9.6 USING THE Q
QUADRATIC
FORMULA
6/page to print
Quadratic formula
ƒ Method
M th d to
t solve
l quadratic
d ti equations
ti
ƒ Slowest method, but works if other
methods
h d fail
f il
ƒ Factoring: integer solutions
ƒ Square Root Property: if it is a perfect
square on the variable side
ƒ Can make it a perfect square by
‘completing the square’
Quadratic formula
ƒ There
Th
is
i a song “Pop
“P G
Goes th
the W
Weasel”
l”
ƒ Can use it to remember the formula
ƒ Negative B plus or minus
ƒ the square
q
root of the quantity
q
y
ƒ B squared minus four A C
ƒ ALL over two A
x= [[— B ± √(B2 — 4 A C) ] / 2A
x
ƒ Equation
E
ti needs
d to
t b
be written
itt iin
standard form
ƒ 0 = Ax
A 2 +Bx
B +C
ƒ Use A, B and C from standard form in the
formula above
ƒ Be sure to pay attention to negative signs!
0= x2 — 14x + 49
0
ƒ A = 1,
1 B = -14,
14 C = 49
− (− 14 ) ±
(− 14) − 4(1)(49)
2(1)
(+ 14) ± (196) − (196)
2
2
14
=7
2
5x2 — x = 2
ƒ 0= 5x2 — x — 2
ƒ A = 5,
5 B = -1,
1 C=—2
− (− 1) ±
(+ 1) ±
(− 1) − 4(5)(− 2)
2(5)
(1) + (40)
1±
10
2
41
10
— 3x2 +5x — 4 = 0
ƒ 3x2 —5x + 4 = 0
ƒ A = 3,
3 B = —5,
5 C=4
− (− 5) ±
(+ 5) ±
(− 5)
2(3)
(25) − (48)
6
2
− 4(3)(4 )
5 ± − 23
=
6
5 ± i 23
=
6
Number of real solutions
ƒ Radical
R di l goes away
ƒ One real solution
(+ 14) ± (196) − (196)
ƒ Plus or minus a value
ƒ Two real solutions
2
1± 41
10
5 ± i 23
=
ƒ Two imaginary solutions
6
ƒ Plus or minus imaginary
Under the radical sign
ƒ The
Th “Discriminant”
“Di i i
t”
ƒ Value > 0: two real solutions
ƒ Value = 0: one real solution
ƒ Value < 0: two imaginary
g
y solutions
Group exploration page 535
ƒ x2 +5x
5 +6=0
ƒ Factor
ƒ Complete the square
ƒ Q
Quadratic formula
ƒ Which is easier?
Group exploration page 535
ƒ x2 +4x
4 —7=0
ƒ Factor
ƒ Complete the square
ƒ Q
Quadratic formula
ƒ Which is easier?