Algebra 2: Chapter 6
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y  a ( x  h) 2  k
Family of Parabolas
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y
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1. Graph y = x2 on the axis to the right. Use the “2nd-TABLE”
key to be precise with graphing each point.
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2. Now graph the equation y = x +4 on the same axis. What
has changed from y = x2?
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3. Now graph y = x2 – 2. What has changed from y = x2?
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x
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4. Graph y = x2 on the axis to the right. Use the “2nd-TABLE”
key to be precise with graphing each point.
y
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5. Now graph y = (x + 4)2 on the same axis. What has changed
from y = x2?
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6. Now graph y = (x – 2)2. What has changed from y = x2?
x
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7. Graph y = x2 on the axis to the right. Use the “2nd-TABLE”
key to be precise with graphing each point.
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8. Now graph y = –x2 on the same axis. What has changed
from y = x2?
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y
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9. Now graph y = 2x2. What has changed from y = x2?
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10. Now graph y = 0.5x2. What has changed from the original y
= x2?
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x
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Parent graph: y  x 2 is called the parent graph for quadratics. It has a vertex at (0, 0) and one
solution when x = 0.
Vertex Form: y  a( x  h) 2  k is called vertex form of a quadratic. The vertex of this
quadratic is (h, k ).
If a is negative the quadratic is flipped
If a is between 0 and 1 it will make the parabola wider
If a is bigger than 1, then it makes the parabola more narrow (skinnier)
If h is positive the vertex is moved left
If h is negative the vertex is moved right
If k is positive the vertex is moved up
If k is negative the vertex is moved down
Graph the following functions by hand
y  x2  5
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y  ( x  3)2
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y   x  1  2
2
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y    x  1  6
2
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y   x  3  2
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y   x2  1
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2
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y  x2  6 x  8
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y  2( x  1)2
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y  x2  4x  7
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y  2  x  4   6
y  x2  4x  5
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y  2 x2  4
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2
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