Algebra 1 notes
Howtofindthevente
Is theVertextheMaximum
É
equal to zero becausethereis a con Ifthesquaredtermisstunt lyintercept negative thegraph5,0and 3,0 1 opens downward
7in't Is't t.fi ptttn t X t 30x
i
the ycoordinateofthe takethecoefficientof
5 3 2 the nonsquared term
Divide thatanswervertex
30O and0,0by2 x coordinate 1 16 If the
gtp p'ing
of the vertex you'vefoundthevertex'stoo x coordinatesof
x intercepts zeroes downwardthevertex
isthemaximum
1 30 0 30
Divide thatanswer
Plugthat infor X t 2x 15
by2 x coordinate
x togettheycoo of the vertex Ifthesquaredtermisroinateof thevertex
511713
solve theequation
I
a
x togettheycoo
4 4 16 roinateof thevertex
If thegratinp
Ii
t.ttYou'vefoundtheVertex 152 3065 wardthevertex
solve theequation istheminimum
225 450 675
You'vefoundtheVertexg
changeequation to
standardform
2 2 75Is thevertextheMaximum
formstepsabove
Followthestandard
sid.FI t
thevertexarelessthan
iii
thevertex'syvaluethe theVertex's
yvalvethe theconstanttermin the
n.fi
T
graphopensdown equationistheyintercept Changeequation to
standardform
jjijjjjjj.it0,15 2 2 75
THEM Ii Followthestandard
formstepsabove
downwardthevertex upwardthevertex
istheminimum
seefindingthreepointsonagraph
Endingthreepointsonagath Makeyourgraph
nm
i iiFindthevertexoftheequation
ii Ii
5,0and 3,0
addthexcoordinatesofthezeroes the
5 3 2 22 1 Plotthethreepointsyoufound on it
Plugthat infor x togettheycoo
roinateof thevertex
511713
4 4 16
thevertex isoneofyour
threepoints Draw alinethroughallyourpoints
There arethreedifferentwaystofind t.ii.irtwo mo e points
t t t t it
t.tt mg i
Goand eo
5 X x 3 5 3 3 3
whatmakeparenthesis
forone ofyourpoints
µ g g
d
3
solveforywiththat x valve
µ 53 3 3
2 9
18
findtheyintercept thisis
you ycoordinate forbothof
yourother twopoints2 2 75 13,18 and 18
takethat xvalveandsubtractitfromthe
0,15
t
x coordinateofthevertex
Thisis
you ycoordinate forboth 1 3 2ofyourothertwopoints this isyourx coordinateforyourfinal
10,75 and 17,751 point
Takethat xvalveandsubtractit
fromthex coordinateofthevertex
0 7 7
this isyourx coordinateforyourfinalpoint
0,75and 11,15