Quadratic Formula Review

Many trinomials can be factored with

integer solutions (roots).

(what factor pair of 7 has a SUM of +8 ?)
x2 + 8x + 7  = 0

(x + 7) (x - 1)

(x + 7) (x + 1)

(x - 7) (x - 1)

(what factor pair of 5 has a SUM of +8 ?)

Other trinomials CANNOT be factored with

integer solutions (roots).

x2 + 8x + 5  = 0

+5 and +1

-5 and -1

 NONE

             Some trinomials like x2 + 8x + 5 = 0

 do not factor smoothly (the answers are not integers).

When this happens, use the QUADRATIC FORMULA:
The coefficient (the number in front) of x2 is "a"
The coefficient (the number in front) of xis "b"
QUADRATIC FORMULA:
The constant (a number by itself) is "c"

a

x2 +  x +    = 0

b

c

a = 1     b = 8     c = 5

1

The coefficient (the number in front) of x2 is "a"
The coefficient (the number in front) of xis "b"
x2 +  x +    = 0
The constant (a number by itself) is "c"

a

x2 +  x +    = 0

8

b

5

c

Plug these values

into the

quadratic formula

Quadratic Formula:
a =          b =         c =

x2 + 15x + 26 = 0

Fill in the blanks

a =

b =

c =

Plug the a,b, and c values into the quadratic formula:
-

1

15

26

x2 + 15x + 26 = 0

2

Quadratic

Formula:

*
2
-
4
*
*
Quadratic Formula:
a =          b =         c =

4x2 - 15x + 2 = 0

Fill in the blanks

a =

b =

c =

Plug the a,b, and c values into the quadratic formula:
-

4

-15

2

4x2 - 15x + 2 = 0

2

Quadratic

Formula:

*
2
-
4
*
*
Quadratic Formula:
a =          b =         c =

x2 + 2 = 0

Fill in the blanks

a =

b =

c =

Plug the a,b, and c values into the quadratic formula:
-

1

0

2

x2 + 2 = 0

2

Quadratic

Formula:

*
2
-
4
*
*
Quadratic Formula:
a =          b =         c =

7x- 2x  = 0

Fill in the blanks

a =

b =

c =

Plug the a,b, and c values into the quadratic formula:
-

7

-2

0

7x- 2x  = 0

2

Quadratic

Formula:

*
2
-
4
*
*
a = 1     b = 8     c = 5

1

The coefficient (the number in front) of x2 is "a"
The                      (a number by itself) is "c"
The                      (the number in front) of xis "b"
x2 +  x +    = 0
coefficient
?
constant
?

a

x2 +  x +    = 0

8

b

5

c

quadratic
?

Plug these values

into the

               formula

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