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