-5 5 10
-10
-5
5
x
y
-5 5 10
-10
-5
5
x
y
GraphingQuadraticFunctionsinStandardForm
Name:_______________________________Date________________
Example: Graph
2
45yx x
Step1:Findtheaxisofsymmetry
4
2(1)
2
x
x

Step2:Findthevertex
2
45
24(2)5
485
9 (When x=2)
yx x
y
y
y




Step3:Findthey‐intercept
2
2
2
45
()
4(5)
5
yx x
y
abxc
yx x
c




Step4:Findtwomorepointsonthesamesideoftheaxisofsymmetryasthepointcontainingthey‐intercept.
2
2
2
45
4(5)
yx x
ya bxc
yx x



Twootherpointsare(1,‐8)and(‐1,0)
Step5:Graphtheaxisofsymmetry,thevertex,thepoint containingthey‐intercept
andtwootherpoints
Step6:Reflectthepointsacrosstheaxisofsymmetry.
Connectthepointswithasmoothcurve.
Use
2
b
x
a

.Substitute1foraand‐4forb.
Simplify
Note:thisisaverticalline
Thex‐coordinateofthevertexis2.Substitute2
forx
They‐coordinateis‐9.Sothepointis(2,‐9)
Identifycintheequation
2
()
y
abxc
Sothepointis(0,‐5)
Sincetheaxisofsymmetryisx=2,choose
valueslessthan2.
Thiswillallowustousethesymmetryofthe
parabolatosketchthegraph.
Letx=1
y=1
2
‐4(1)‐5
=1‐4‐5
=‐8
Letx=‐1
y=(‐1)2‐4(‐1)‐5
=1+4‐5
=0
-8-6-4-2 2468
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
-8-6-4-2 2468
-6
-4
-2
2
4
6
8
10
12
x
y
-8-6-4-2 2468
-8
-6
-4
-2
2
4
6
8
x
y
-6 -4 -2 2 4 6
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
-10-8-6-4-2 2 4 6 810
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
-4 -2 2 4
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
GraphingQuadraticFunctionsinStandardFormWorksheet#1
Name:______________________________________Period____________Date_____________
Directions:Graphtheseequations.Identifytheaxisofsymmetry,vertex,andy‐intercept.
1.)
2
23yx x2.)
2
3129yx x

3.)
2
64yx x 4.)
2
48yx

5.)
2
1
6
4
yxx
6.)
2
225
y
xx
