Parabola and its Intercepts

There are 2 intercepts to calculate :

y – intercept where x = 0

substitute x = 0 into the equation and solve for y

x – intercepts where y = 0 ( sometimes there are NONE )

Two ways to solve :

a) Factoring Method

b) Quadratic Formula

a

acbbx

2

42

x - intercepts

y - intercept

cbxax 2

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

862 xxy

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept - substitute x = 0 and solve for y

862 xxy

8

800

8060

862

2

y

y

y

xxy

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 8 )

862 xxy

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 8 )

x – intercept - is the equation factorable ?

- are there 2 factors of 8 that add/sub = 6 ?

862 xxy

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 8 )

x – intercept - is the equation factorable ?

- are there 2 factors of 8 that add/sub = 6 ?

YES

862 xxy

624 and 824

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 8 )

x – intercept

YES

862 xxy

624 and 824

24

862

xxy

xxy Factoring Method…

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 8 )

x – intercept

- set y = 0 and solve for x

862 xxy

240

24

862

xx

xxy

xxy Factoring Method…

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 8 )

x – intercept

862 xxy

240

24

862

xx

xxy

xxy

2 4

02 04

xx

xx

Factoring Method…

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 8 )

x – intercept = ( - 4 , 0 ) and ( - 2 , 0 )

862 xxy

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

153 2 xxy

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept - substitute x = 0 and solve for y

153 2 xxy

1

100

1)0(5)0(3

1532

2

y

y

y

xxy

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0, 1 )

153 2 xxy

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0, 1 )

x – intercept - this equation is not factorable

153 2 xxy

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0, 1 )

x – intercept - this equation is not factorable

QUADRATIC FORMULA

153 2 xxy

a

acbbx

2

42

a = 3

b = - 5

c = 1

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0, 1 )

x – intercept

QUADRATIC FORMULA

153 2 xxy

6

135

6

12255

32

1345)5(

2

42

2

x

a

acbbx

a = 3

b = - 5

c = 1

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0, 1 )

x – intercept =

153 2 xxy

0 ,

6

135- You can keep your answer like this

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0, 1 )

x – intercept =

153 2 xxy

0 ,6

135,0 ,

6

135

0 ,6

135

- Or split it up like this

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0, 1 )

x – intercept =

153 2 xxy

0 , 23.0, 0 , 43.1

0 ,6

135, 0 ,

6

135

0 ,6

135

- Or use decimals, round to 2 places

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

325 2 xxy

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept

325 2 xxy

3

300

30205 2

y

y

y

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 3 )

325 2 xxy

3

300

30205 2

y

y

y

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 3 )

x – intercept

325 2 xxy

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 3 )

x – intercept

Equation is not factorable, use quadratic formula

325 2 xxy

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 3 )

x – intercept

Equation is not factorable, use quadratic formula

325 2 xxya = 5

b = 2

c = 3

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 3 )

x – intercept

Equation is not factorable, use quadratic formula

325 2 xxya = 5

b = 2

c = 3

10

562

10

6042

52

35422

2

422

x

a

acbbx

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 3 )

x – intercept

Equation is not factorable, use quadratic formula

325 2 xxya = 5

b = 2

c = 3

10

562

10

6042

52

35422

2

422

x

a

acbbx

Undefined, therefore there are NO x - intercepts

Parabola and its Intercepts

EXAMPLE : Find the x and y intercepts for the parabola whose equation

is defined as :

y – intercept = ( 0 , 3 )

x – intercept = NONE

325 2 xxy

10

562

10

6042

52

35422

2

422

x

a

acbbx

Undefined, therefore there are NO x - intercepts