Converting Vertex Form Equations to Standard Form
February 28, 2013
What's Going On?
Expanding Binomials
Expanding 2.0
Practice
Learning Goal ­ I will be able to change quadratic relations from vertex form to standard form!
1
Converting Vertex Form Equations to Standard Form
February 28, 2013
Expanding Binomials Review
Multiply these two binomials (expand)
(x ­ 4)(2x + 1)
2
Converting Vertex Form Equations to Standard Form
February 28, 2013
Expanding Binomials
Expand.
Huh?
2
(x + 4) 3
Converting Vertex Form Equations to Standard Form
February 28, 2013
Expanding Binomials
Expand.
2
(x + 4) When we see something
squared,
we know it means
"that thing times itself"
The same is true here!
In this case, "that thing"
is (x
+ 4)
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Converting Vertex Form Equations to Standard Form
February 28, 2013
Expanding Binomials
Expand.
2
(x + 4) (x + 4)(x + 4) 5
Converting Vertex Form Equations to Standard Form
February 28, 2013
Standard Form Equations
Last unit we dealt with lots of quadratics (parabolas) in vertex form
Vertex Form: y = a(x ­ h)2 + k
This unit we are going to look at quadratics in standard form as well!
Standard Form: y = ax2 + bx + c
6
Converting Vertex Form Equations to Standard Form
February 28, 2013
Standard Form Equations
Consider this parabola:
We know that the vertex
form equation is:
y = (x - 2)2 - 5
In this case, the
standard form equation is:
y = x2 - 4x -1
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Converting Vertex Form Equations to Standard Form
February 28, 2013
Expanding 2.0
Today we have learned that quadratics can
be represented in
vertex form: y = a(x - h)2 + k
and in
standard form: y = ax2 + bx + c
The a in each is the same! In fact, it gives
us the step pattern no matter which
equation we look at.
What about the c in the standard form
equation?
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Converting Vertex Form Equations to Standard Form
February 28, 2013
Expanding 2.0
standard form: y = ax2 + bx + c
What about the c in the standard form
equation?
It's the y­intercept!
It's where the parabola crosses the y­axis!
9
Converting Vertex Form Equations to Standard Form
February 28, 2013
Standard Form Equations
Consider this parabola:
We know that the vertex
form equation is:
y = (x - 2)2 - 5
In this case, the
standard form equation is:
y = x2 - 4x -1
y­intercept
10
Converting Vertex Form Equations to Standard Form
February 28, 2013
Expanding 2.0
We can actually change any vertex form equation into standard form using some pretty easy math!
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Converting Vertex Form Equations to Standard Form
February 28, 2013
Expanding 2.0
Change the following into standard form.
y = (x - 3)2
To do this we will need to use the skills from yesterday!
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Converting Vertex Form Equations to Standard Form
February 28, 2013
Converting from Vertex Form to Standard Form
1. Change the (x - h)2 part of the
vertex form equation to
(x - h)(x - h).
2. Use FOIL to expand
(x - h)(x - h) into a new set of
brackets. Be sure to simplify!
3. Multiply through the new set of
brackets by a.
4. Collect like terms and simplify.
*Make sure you have your new
equation in the correct order:
ax 2 + b x + c
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Converting Vertex Form Equations to Standard Form
February 28, 2013
Converting from Vertex Form to Standard Form
1. Change the (x - h)2 part of the
vertex form equation to
(x - h)(x - h).
2. Use FOIL to expand
(x - h)(x - h) into a new set of
brackets.
3. Multiply through the new set of
brackets by a.
4. Collect like terms and simplify.
*Make sure you have your new
equation in the correct order:
ax2 + bx + c
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Converting Vertex Form Equations to Standard Form
February 28, 2013
Convert to standard form.
2
y = 3(x + 2) - 2
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Converting Vertex Form Equations to Standard Form
February 28, 2013
Convert to standard form.
2
y = -0.5(x - 4) + 13
a = ___, b = ___, c = ___
the y­intercept is ___
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Converting Vertex Form Equations to Standard Form
February 28, 2013
Expanding 3.0
Determine the standard form equation of the
given quadratic.
a = 2, vertex at (1, 3)
uhoh!
We need the stuff from last unit to get the vertex form equation first!
then we just use the steps from today!
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Converting Vertex Form Equations to Standard Form
February 28, 2013
Write each in standard form.
State the vertex and y-intercept for each.
1. y = (x + 6)2
5. y = (x - 8)2 + 3
2. y = (x - 1)2
6. y = 5(x - 4)2 + 12
3. y = 3(x + 9)2
7. y = 0.5(x - 6)2 - 11
4. y = -0.25(x + 8)2
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Converting Vertex Form Equations to Standard Form
February 28, 2013
Write each in standard form.
State the vertex and y-intercept for each.
1. y = (x + 6)2
a = ___, b = ___, c = ___
the y­intercept is ___
19
Converting Vertex Form Equations to Standard Form
February 28, 2013
Write each in standard form.
State the vertex and y-intercept for each.
2
2. y = (x - 1)
a = ___, b = ___, c = ___
the y­intercept is ___
20
Converting Vertex Form Equations to Standard Form
February 28, 2013
Write each in standard form.
State the vertex and y-intercept for each.
3. y = 3(x + 9)2
a = ___, b = ___, c = ___
the y­intercept is ___
21
Converting Vertex Form Equations to Standard Form
February 28, 2013
Write each in standard form.
State the vertex and y-intercept for each.
2
4. y = -0.25(x + 8)
a = ___, b = ___, c = ___
the y­intercept is ___
22
Converting Vertex Form Equations to Standard Form
February 28, 2013
Write each in standard form.
State the vertex and y-intercept for each.
2
5. y = (x - 8) + 3
a = ___, b = ___, c = ___
the y­intercept is ___
23
Converting Vertex Form Equations to Standard Form
February 28, 2013
Write each in standard form.
State the vertex and y-intercept for each.
2
6. y = 5(x - 4) + 12
a = ___, b = ___, c = ___
the y­intercept is ___
24
Converting Vertex Form Equations to Standard Form
February 28, 2013
Write each in standard form.
State the vertex and y-intercept for each.
7. y = 0.5(x - 6)2 - 11
a = ___, b = ___, c = ___
the y­intercept is ___
25