Warm–up #101. Solve

(u – 8)(u + 8) = 0(

Let

Solve by Factoring1.

1

x + 1 = x – 1 =

1 1 1 1

Homework LogThurs

10/15

Lesson 2 – 5

Learning Objective: To solve quadratic equations by quadratic formula

Hw: #211 Pg.135 #1 – 23 odd

Homework LogFri

10/16

Lesson 2 – 5

Learning Objective: To use discriminant to determine types of roots

Hw: #212 Pg.136 #25 – 51 odd WS # 11 – 14

10/15/15 Lesson 2 – 5 Quadratic Formula Day 1

Advanced Math/Trig

Learning Objective

To solve quadratic equations by quadratic formula

2 4

2

b b acx

a

Quadratic Formula

Xavier is a negative boy who couldn’t decide (yes or no) whether to go to a radical party.

It turns out that this boy is a total square because he missed out on 4 awesome chicks.

And the party was all over at 2 AM.

2Given: 0ax bx c

Solve by Quadratic Formula

1.

Set = 0

a = 9 b = 7 c = –1

Solve by Quadratic Formula

2.

Distribute & Set = 0

a = 1 b = 2 c = –168

{12, –14}

Solve by Quadratic Formula

3.

{− 12± 𝑖}{− 1±2 𝑖

2 }

10/16/15 Lesson 2 – 5 Discriminant Day 2

Advanced Math/Trig

DiscriminantDiscriminant – tells the nature of the roots

(Part under the radical)

Discriminant Roots

Zero 1 real double root

Positive 2 real roots

Negative 2 imaginary roots

DiscriminantUse the discriminant to determine the nature of the roots.

1.

a = 2 b = –1 c = –15

= 121

= = 1 + 120

2 Real Roots

DiscriminantUse the discriminant to determine the nature of the roots.

2.

a = 4 b = –20 c = 25

= 0

= = 400 – 400

1 Real Double Root

DiscriminantUse the discriminant to determine the nature of the roots.

3.

a = 1 b = 4 c = 13

= –36

= = 16 – 52

2 Imaginary Roots

DiscriminantDetermine k so that the roots are equal real roots.

4.

k=±2√30

2 real equal roots, so discrim = 0

a = 6 b = k c = 5

Sum-Product RuleGiven 2 roots, we can write the quadratic equation:

x2 – (sum)x + product = 0

5. Determine a monic quadratic eq’n if the sum of its roots is –2 and the product of its roots is –8.

x2 – (sum)x + product = 0 x2 – (–2)(x) + –8 = 0

x2 + 2x – 8 = 0

leading coeff = 1

Sum – Product Rule

x2 – (sum)x + product = 0

sum: 0 + –3 =

–3

product: (0)(–3) =

0

x2 – (–3)(x) + 0 = 0

x2 + 3x = 0 equation better have = sign

6. Find a monic quadratic eq’n whose roots are 0 & –3

Sum – Product Rule

x2 – (sum)x + product = 0

sum: + =

product: =

x2 – ()(x) + = 0

7. Find a monic quadratic eq’n whose roots are &

(10)( )

(10)

Sum – Product Rule

x2 – (sum)x + product = 0

sum: + =

product: =

x2 – ()(x) + = 0

8. Find a quadratic eq’n whose roots are &

(3)( )

(3)

Ticket Out the Door

Solve by quadratic formula

Homework

#211 Pg.135 #1 – 23 odd

Homework

#212 Pg.136 #25 – 51 odd

WS # 11 – 14