CPMSection 9.4A

Quadratic Formula

Thus far we have considered two methods for solving quadratic function- factoring and using

the square root property. Each of these methods have their drawbacks however. We

will now consider the……

Quadratic Formula: For the equation , any solutions are given by the formula

X=2 4

2

b b ac

a

153 13 40 02x x 153 13 40a b c

213 (13) 4(153)( 40)

2(153)

13 24649

306

13 157

306

144 170

306 306and

8 5

17 9x and

3 10 1 02x x 3 10 1a b c

210 (10) 4(3)(1)

2(3)

10 100 12

6

10 88

6

10 4 22

6

10 2 22

6

5 1 22

3

2 3 5 02x x

2 3 5a b c

23 ( 3) 4(2)(5)

2(2)

3 9 40

2(2)

No Solution. Can’t have a negative number in the radical

3 31

4

The expression is called the _____________, and it determines home many solutions (0, 1, or 2) the quadratic equation has in the set of real numbers. If , the quadratic has ____ solutions in If , the quadratic has ____ solutions in If , the quadratic has ____ solutions in

discriminant

2 4 0b ac

2 4 0b ac

2 4 0b ac

0

1

2

Find the number of solutions for the following quadratic equations

a a2 12 32 0 2 13 72b b y y2 4 4

2(12) 4(1)(32)

144 128

16disc

2 .real sol

22 13 7 0b b

2( 13) 4(2)( 7)

169 56

225

2 .real sol

2 4 4 0y y 2( 4) 4(1)(4)

16 16

01 .real sol