Quadratic Formula: gives the solution of in terms of the coefficients a, b & c.

2 0ax bx c

a

acbbx

2

42

a

The solutions of the quadratic equation are

a

a

c

c

bb

b

Ex: 1 Solve x2+ 9x +14 = 0

a

acbbx

2

42

a =

b =

c =

12

141499 2

1st

12

1414819

2nd

2

56819

2

259

2

59

2

59

2

59 and

2

14

2

4 and 7 2 and

Ex: Solve x2- 6x +10 = 0

a

acbbx

2

42

a =1

b =-6

c =10

26 ( 6) 4 1 10

2 1

1st

6 36 4 1 10

2 1

2nd 6 36 40

2

6 4

2

6 2

2

i

6 2 6 2

2 2

i iand

3 3i and i

0483 2 xWe must solve to get x2 by

itself 1st!

483 2 x

162 x

4x

6x2 – 11x + 3=0

(2x (3x– 1) = 0– 3)

x = 3/2 x = 1/3

Solve:

6x2 – 11x + 3(2x (3x– 1) – 3)

Write the following quadratic in factored form:

y=6x2 – 11x + 3

Find the x-intercepts for:

y=6x2 – 11x + 3

Find the roots for:

y=6x2 – 11x + 3

For the following quadratic, state the nature of the roots:

a. 2 real solutions

b. 1 complex solution

c. 1 real solution

d. 2 complex solutions

Solve

1) x2 + 5x + 6 = 0

2) x2 + 7x + 6 = 0

3) 6x2 + 15x = 0

x = 1/3, -2

Find the zeroes of the function.

2( ) 3 5 2f x x x

Famous cliff diver Robbie Jarvis dives off of a 138 foot cliff. After t seconds, his

height h (in feet) is modeled by:

h = -16t2 + 138

How many seconds does it take him to reach the water?

Bonus:

Will there be a splash?t = 2.94 seconds