-
7/30/2019 parabolas.ppt
1/9
Parabolas
We can plot this using points
Use replay function on grey calculatorsAnd table function on
green calculators
x -3 -2 -1 0 1 2 3
y=x2 9 4 1 0 1 4 9
y
x1 2 3 4 5 6
1
2
3
4
5
6
1234567
89
10
1
2
We can see that the shape isup 1 out 1up 3 out 1up 5 out 1
up 7 out 1 etc
OrStarting at the vertexOut 1 up 12Out 2 up 22Out 3 up 32Out 4
up 42
y
x
Any equation, where the highest power of x, is x2
when plotted on a graph, will form a parabola
The simplest parabola is 2y x
-
7/30/2019 parabolas.ppt
2/9
y
x1 2 3 4 5 6
1
2
3
4
5
6
12
1
2 3 4 5 6 7
8 9
10
2try y x
x -3 -2 -1 0 1 2 3
y = -x2 -9 -4 -1 -0 -1 -4 -9
The graph is the sameshape but upside-down
The negative signreflects the graph in thex axis
-
7/30/2019 parabolas.ppt
3/9
y
x
y
x
y
x
y
x1 2 3 4 5 6 1 2 3 4 5 6
1
2
3
4
5
6
7
8
9
10
11
1213
14
15
1
2
2y x We can see the larger the
number in front of the x2The steeper the graphRemember the
gradient oflinear graphs got steeperif we increased thenumber by
the x
These graphs arebest plotted usingpoints
y
x
2We can try putting other numbers infront of the x22y x
23y x25y x
-
7/30/2019 parabolas.ppt
4/9
y
x1 2 3 4 5 6
1
2
3
4
5
6
1
2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
y
x
2y x
The graph is still reflected inthe x axisWe can see the larger
thenumber in front of the x2
The steeper the graphRemember the gradient oflinear graphs got
steeper ifwe increased the number bythe x
y
x
y
x
y
x
2We can try putting other numbers infront of the x22y x
23y x 25y x
-
7/30/2019 parabolas.ppt
5/9
y
x1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
78
9
10
1
2
3
4
5
6
7
8
9
10
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
The smaller the number infront of the x2 the flatter
thegraph
The ones with negative signare reflected in the x axis
2y x
21
2y x
21
4y x
2We can try putting a smaller number in front of the x
21
10y x
2y x
21
2y x
214
y x
21
10y x
2
-
7/30/2019 parabolas.ppt
6/9
y
x1 2 3 4 5 6 1 2 3 4 5 6
1
2
3
4
56
7
8
9
10
1
2
3 4
5
6
7
8
9
10
We can see:If we add a number to the x2the parabola shifts upIf
we subtract a number fromthe x2 the parabola shiftsdown
Note the shape is thebasic 2y x
Remember the correct word for shift is translate
2y x
2 3y x 2 1y x 2
5y x
2 7y x
y
x
y
x
y
x
y
x
y
x
-
7/30/2019 parabolas.ppt
7/9
We can also add numbers to the x before it is squared
2( 4)y x
We can see the shape is the basic x2 shapeIf we add a number in
the brackets thegraph is translated to the minus numberIf we
subtract a number in the bracketsthe graph is translated to the
plus number
Equation of axis is 0x y
2( 3) 0x
( 3) 0x
3x
?Why
2y x
2
( 3)y x
2( 5)y x
2
( 1)y x
y
x1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
1
23
4
5
6
7
8
9
1011
12
13
14
15
1
2
y
x
y
x
y
x
y
x
y
x
-
7/30/2019 parabolas.ppt
8/9
If we add a number in the brackets and at the end the graph is
translatedvertically and horizontally
y
x1 2 3 4 5 6 1 2 3 4 5 6 7 8
1
23
4
5
6
7
8
9
10
1
2
3
4
5
2( 4) 1y x
2
( 3) 4y x
2( 2) 5y x
2( 1) 2y x
y
x
y
x
y
x
y
x
-
7/30/2019 parabolas.ppt
9/9
y
x1 2 3 4 5 6 7 8 1 2 3 4 5 6
1
2
34
5
1
2
3 4
5
6
7
8
9
10
We can also translate the reflected graphs
2 2In general ( ) translates the basic
horizontally verticto ally
graph
tand ok
y x k h y
h
x
2 4y x
2( 5)y x
2( 2) 3y x
y
x
y
x
y
x
