CPM Section 9.4A Quadratic Formula. Thus far we have considered two methods for solving quadratic...
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Transcript of CPM Section 9.4A Quadratic Formula. Thus far we have considered two methods for solving quadratic...
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