Solving Quadratic Equations using the Quadratic FormulaGeneral equation of a quadratic: 02 cbxax

Quadratic Formula:

a

acbbx

2

42 Notice where the

letters come from for the formula

We use the quadratic formula when something can not be factored. However, it also works for factorable quadratic equations as well.

You must get equation equal to zero before you determine a,b, and c.

01382 xx

13

8

1

c

b

a

a

acbbx

2

42

12

131488 2 x

2

128x

2

328x

34x

Before you can find a,b, and c, you must get equation = to 0.

Type what is under the radical exactly as written on your calculator.

053 2 x

5

0

3

c

b

a

a

acbbx

2

42

32

53400 2 x

6

600x

6

152x

3

15x

Solve the quadratic equation by using the quadratic formula and leave answers in simplest radical form.

Solve the quadratic equation by using the quadratic formula and round answers to the nearest hundredth.

029122 xx

29

12

1

c

b

a

a

acbbx

2

42

12

29141212 2 x

2

2812x

2

2812x

2

2812 x

64.8x 35.3x

xx 1082

8

10

1

c

b

a

a

acbbx

2

42

12

8141010 2 x

2

6810x

x10 x10

08102 xxSolve the quadratic equation by using the quadratic formula and round answers to the nearest hundredth.

2

6810x

2

6810 x

12.9x 87.x

Solve the quadratic equation by using the quadratic formula and round answers to the nearest hundredth.

123 xx163 2 xx

1 1

0163 2 xx

1

6

3

c

b

a

a

acbbx

2

42

32

13466 2 x

6

486x

6

486x

6

486 x

15.2x 15.x

762 2 xx Complex Solutions