11/18/2010
Algebra 2 A
Section 5.7
Vertex form of a
Quadratic
Vertex form of a Quadratic
y ax h
2
k
Remember the line
of symmetry?
h is the x-coordinate of the vertex
The horizontal translation (slide)
x
k is the y coordinate of the vertex
The vertical translation (slide)
b
2a
that’s now
x=h
a tells us 2 thing
1. If a is positive the parabola opens up
If a is negative the parabola opens down
2. How wide it opens
a > 1 opens narrow
a < 1 opens wide
The vertical stretch
or shrink
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Identify (h, k) and a.
Describe what they did to y x 2
And the line of symmetry
y
y
1
x 82 2
2
3x 5
2
y 1x 5
4
2
Answers are:
( 8, 2) x = 8
Slide it right 8 up 2 and made it
wider and up side down
(5, -4)
x=5
Slide it right 5 down 4 and made it
narrower
(-5, 0)
x = -5
Slide it left 5
Write the equation in vertex form
y ax h
2
k
Find the h and k first
then find the a
We need only the vertex
and another point
and some algebra
answer
y
7
x 4
4
2
7
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If needed…..
Write an equation for the
parabola shown in the graph.
y ax h2 k
Find the h and k first
then find the a
answer
y
1
2
x 1 2
2
Write the equation in vertex form
y ax h
2
k
From the graph find the h and k
Then find the a using a know
point like (0, 4)
y
y
1
x 32 1
3
a x 3
4 a0 3
1
a
3
2
2
1
1
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Graph Quadratic from Vertex Form
Without a calculator
1.) Find (h, k)
2.) make a table
use zero for x
use zero for y
1.)
y
2.)
y
3x 2
2
12
( to find the y-intercept)
( to find the x intercept (s))
Then solve for y , if I ask you to put
into standard form
4 x 12 7
Going backwards…..
Convert the standard form
in to vertex form without graphing
By Complete the Square
1.)
2.)
y
3x 2 12x
y
4 x 2 8x 3
Then find the vertex points, lines of symmetry,
and does it open or down?
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Convert the standard form
in to vertex form without graphing
By Complete the Square
3x 2 12x
y
y
3
y
3
3x
3
___
2
x
2
y
4
3
12 x
3
y
3
4 x ___
y
4 x2 4x 4
3
y
x 2
2
x 2
3x 2
2
2
4
12
Convert the standard form
in to vertex form without graphing
By Complete the Square
1.)
2.)
y
y
3x 2 12x
4 x 2 8x 3
answers
1.)
y
2.)
y
3x 2
2
12
4 x 12 7
So what are the vertex points, lines of symmetry,
and does it open or down?
1.) vertex ( 2, 12) DOWN and the line of symmetry is x = 2
2.) vertex ( -1, -7) UP and the line of symmetry is x = -1
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Test next Tuesday/Wednesday
Homework
Practice Ws 5.7 #2-8 even, 10-18
Things changed
1st hour especiallly is struggling
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Car rolling activity
Skipped in 2010 due to time
Similar to what they say on page 293
But we are going to bounce balls instead.
I had trouble using cars and ramps to get the data
we need.
Homework
(day one)



Pg 290 # 4,14,21,22,27,28,30
1st hour we are behind either no review
for next weeks test, no review for the
exam, or do all of this in 1 day
??
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