10-6 Using the Quadratic Formula

What is it?

The quadratic formula is a method for solving quadratic equations in the for ax2 + bx + c.

a

acbbx

2

42

Let’s try one!Solve using the quadratic

formula. 652 xx a=1, b=-5, c=6 Substitute these values into the

formula:

)1(2

)6)(1(4)5()5( 2 x

2

242525 x

2

125x

2

125x

2

125 x

2

26x

2

24x

13x 12x

Let’s try another one!Solve using the quadratic

formula. 822 xx a=1, b=-2, c=-8

)1(2

)8)(1(4)2()2( 2 x

2

3244 x

2

364x

2

64x

2

64 x

52

10x 1

2

2

x

Rewrite it…

0822 xx

Let’s try another one!Solve using the quadratic

formula. 0253 2 xx a=-3, b=5, c=-2

)3(2

)2)(3(4)5()5( 2

x

6

24255

x

6

15

x

6

15

x6

15

x

3

2

6

4

x 16

6

x

One more!Solve using the quadratic

formula. 0827 2 xx a=7, b=-2, c=-8

)7(2

)8)(7(4)2()2( 2 x

14

22442 x

14

2282x

14

10.152x

14

10.152 x

14

10.17x

22.1x 94.0x

14

10.13x

Choosing the Right Method for Solving Quadratic

EquationsThere are many methods…how to decide?The quadratic formula always works but is not

always the easiest.

Sometimes you can easily see the factors, then factoring is easiest.

Competing the square…is probably more involved than using the quadratic formula.