Luttrell 2012
121
Name: ______________________
Date: _____
8h –Quadratic Formula
All quadratic equations are of the form
y
=
ax
2
+
bx
+
c
, where a, b, and c are real numbers.
When
y
= 0,
y
ou can solve for
x
by factoring or using the quadratic formula. Factoring doesn’t
alwa
y
s work, but the quadratic formula will!
Quadratic Formula:
x
b
b
ac
a
=
− ±
−
2
4
2
E
x
ample A:
x
2
+ 2
x
-3 = 0
Identif
y
parts: a = 1, b = 2, c = -3
Substitute into formula:
x
=
− ±
−
−
=
− ±
=
− ±
2
2
4 1
3
2 1
2
16
2
2
4
2
2
( )(
)
( )
= 1 or -3
Find the solutions (roots, zeros,
x
-intercepts):
1. 5
x
2
+2
x
- 3 = 0
2. 4
x
2
- 3
x
- 7 = 0
3. 4
x
2
+5
x
- 6 = 4
4. 3
x
2
+ 7
x
- 10 = 0
5.
x
2
- 5
x
+ 6 = 0
6. 3
x
2
+ 11
x
- 4 = 0
7. x
2
- 5x - 6 = 0
8. x
2
+ 10x + 21 = 0
9. x
2
- 2x + 2 = 2x
