Graphing Parabolas in Vertex Form
February 14, 2013
What's Going On?
Back to yesterday's stuff.
What's h again?
Vertex Form: y = ±a(x ­ h)2 + k
What's my Equation?
Learning Goal ­ I will be able to graph functions in the form y = a(x ­ h)2 + k.
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Graphing Parabolas in Vertex Form
February 14, 2013
Back to Yesterday's Stuff
Yesterday you learned about h in the equation
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y = a(x ­ h) + k
The value of h moves the parabola left and right. This is called the horizontal shift!
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Graphing Parabolas in Vertex Form
February 14, 2013
Back to Yesterday's Stuff
If you were given this equation:
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y = (x ­ 2) What is the value of h?
Has the parabola been moved left or right?
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Graphing Parabolas in Vertex Form
February 14, 2013
Back to Yesterday's Stuff
If you were given this equation:
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y = (x + 3) What is the value of h?
Has the parabola been moved left or right?
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Graphing Parabolas in Vertex Form
February 14, 2013
Vertex Form Equations
Now that we know what a, h and k do, we are ready to put them together and look at equations in the form.
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y = a(x ­ h) + k
This is called the vertex form equation of a parabola! You will see why in a moment.
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Graphing Parabolas in Vertex Form
February 14, 2013
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y = ±a(x ­ h) + k
±­
If we have a negative sign out front, the parabola
opens downwards. Otherwise, it opens upwards.
a ­
a controls the step pattern. To find the new step
pattern, multiply (1, 3, 5, 7, ...) by a
If a is greater than 1, the parabola is stretched
If a is less than 1, the parabola is compressed.
h­
h controls the horizontal shift
If h is positive, the curve shifts to the right
If h is negative, the curve shifts to the left
k ­
k controls the vertical shift
if k is positive, the curve shifts up
if k is negative, the curve shifts down
vertex: ( , )
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Graphing Parabolas in Vertex Form
February 14, 2013
Vertex From Equations
If we were given a vertex form equation
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y = 2(x ­ 1) ­ 3
What are the coordinates of the vertex?
The x­coordinate is the h value!
The y­coordinate is the k value!
What is the new step pattern?
It's the old step pattern multiplied by a!
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Graphing Parabolas in Vertex Form
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February 14, 2013
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y = x and y = 2(x ­ 1) ­ 3
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