Solving Quadratic Equations using the Quadratic Formula

Objective:

Students will be able to solve quadratic equations by using the quadratic formula

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.

#1: 01382 xx

13

8

1

c

b

a

a

acbbx

2

42

12

131488 2 x

2

128x

3412

32 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.

Simplify the radical

Divide by the denominator, if you can

Zeros:

#2: 053 2 x

5

0

3

c

b

a

a

acbbx

2

42

32

53400 2 x

6

600x

6

152x

15460

152

3

15x

Simplify the radical

Divide by the denominator, if you can. Since I can’t, divide by GCF

Zeros:

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 tenth.

#3: 029122 xx

29

12

1

c

b

a

a

acbbx

2

42

12

29141212 2 x

2

2812x

Since we are solving to the nearest tenth, we do not need to simplify the radical!

2

2812x

2

2812 x

64.8x6.8x

35.3x4.3x

Be careful when typing this into your calculator. I recommend that you type in the numerator then hit enter, then divide by denominator!

Zeros:

#4: 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 tenth.

2

6810x

2

6810 x

12.9x1.9x

87.x9.x

Zeros:

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

#5: 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

15.2x1.2x

15.x2.x

Zeros

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

#6: xx 412 2 x4 x4

0142 2 xx

1

4

2

c

b

a

a

acbbx

2

42

22

12444 2 x

4

84x

248

224

224x

Divide by the denominator, if you can. Since I can’t, divide by GCF

2

22x

Zeros: