Unit 1Bquadratics
Day 4
Graphing a QuadraticFunction
M2 Unit 1B: Day 4
Lesson 3.1B
EQ: How do we graph a quadraticfunction and identify all of itscharacteristics?
Today, we are going to begin by reviewingwhat we have learned about graphingquadratics so far
Lets recall how to find the following:
Vertex
AOS
Maximum or Minimum
Y-intercept
Find: a) vertex
b) axis of symmetry
c) state whether the vertex is a maximum or minimum.
d) y - intercept
a = -2,
b = 4
c = -2
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a) Vertex:
b) Axis of symmetry:
c) Since a < 0 , the parabola opens down and has a:
maximum
(1, 0)
x = 1
d) y-intercept:
(0, -2)
a = 1,
b = 0
c = 2
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Find: a) vertex
b)axis of symmetry
c) state whether the vertex is a maximum or minimum.
d) y-intercept
a) Vertex:
b) Axis of symmetry:
c) Since a > 0 , the parabola opens up and has a:
minimum
(0, 2)
x = 0
d) y-intercept:
(0, 2)
a = -3
h = 1
k = 2
a) Vertex:
b) Axis of symmetry:
c) Since a < 0 , the parabola opens down and has a:
maximum
6
Find: a) vertex
b) axis of symmetry
c) state whether the graph has a maximum or minimum.
d) y - intercept
(1, 2)
x = 1
d) y-intercept:
(0, -1)
Domain VS. Range
Domain: (x – values) read domain from leftto right
Range: (y-values) read range from bottomto top
Last week we said that the DOMAIN of parabolas isall real numbers…unless the parabola looks like thisand has endpoint(s)
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We say the domain is restricted, therefore it is nolonger all real numbers
Find the domain of the graph below
Domain:
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-1 < x < 2
Find the domain of the graph below
Domain:
10
-2 < x < 2
Find the domain of the graph below
Domain:
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Vertex:
Y-intercept:
Axis of symmetry:
One more point:
Domain:
Range:
Max or Min?
Graph the quadratic using the axis of symmetry and vertex.
maximum
All real numbers
y ≤ 3
12
Extrema:
y = 3
Vertex:
Y-intercept:
Axis of symmetry:
One more point:
Domain:
Range:
Max or Min?
Graph the quadratic using the axis of symmetry and vertex.
minimum
All real numbers
y ≥ 0
13
(-1, 0)
Extrema:
y = 0
Vertex:
Y-intercept:
Axis of symmetry:
One more point:
Domain:
Range:
Max or Min?
Graph the quadratic using the axis of symmetry and vertex.
maximum
All real numbers
14
Extrema:
y = 5/4
Stretch VS. Shrink Compare the following graphs and equations:
What is the differencebetween these twographs when comparedto the parent function?
*note: rubber band
Vertical stretch
Vertical shrink
Look at a couple more…
What we should notice and confirm at this point is that the value of “a”determines how wide or narrow the graph will be…
When a is greater than 1, we call that a vertical stretchWhen a is less than 1, we call that a vertical shrink
State whether the graph shows avertical stretch or vertical shrink
Shrink…so |a| < 1
Stretch…so |a| > 1
Stretch…so |a| > 1
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Intervals of
increase and decrease
To determine the intervals of increase and decrease,you must “read” the graph from left to right
What are theselines doingfrom left toright?
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Let’s apply this idea to parabolas…
To determine the intervals of increase and decrease,you must “read” the graph from LEFT to RIGHT
What is thisparabola doingon the left side ofthe vertex?
Going downhill
What is thisparabola doingon the rightside of thevertex?
Going uphill
Interval of decrease
Interval of increase
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One more…
What is thisparabola doingon the left sideof the vertex?
Going uphill
What is thisparabola doingon the rightside of thevertex?
Going downhill
Interval of decrease
Interval of increase
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Graph each quadratic function and determinethe interval of increase and decrease
Interval of decrease
Interval of increase
y = -2x² + 12x - 14
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Interval of decrease
Interval of increase
Graph each quadratic function and determinethe interval of increase and decrease
y = x² + 2x + 3
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Interval of decrease
Interval of increase
Graph each quadratic function and determinethe interval of increase and decrease
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Determine if the given interval is an interval ofincrease or decrease
decrease
increase
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Determine if the given interval is an interval ofincrease or decrease
increase
increase
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Assignment: Day 2 Handout
