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Today, we are going to begin by reviewing what we have learned about graphing quadratics so far Lets recall how to find the following: Vertex AOS Maximum or Minimum Y-intercept
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Unit 1Bquadratics
Day 4
Graphing a Quadratic Function
M2 Unit 1B: Day 4
Lesson 3.1B
EQ: How do we graph a quadratic function and identify all of its
characteristics?
Today, we are going to begin by reviewing what we have learned about graphing
quadratics so farLets 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
21. ( ) 2 4 2 f x x x a = -2, b = 4 c = -2
2bxa
4
2 2x
1x
2(1) 2 1 4 1 2f (1) 0f
4
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 = 22bxa
0
2 1x 0x
2(0) 0 2f (0) 2f
22. ( ) 2f x x
5
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
23. ( ) 3( 1) 2f x x
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 left
to right Range: (y-values) read range from bottom
to top
Last week we said that the DOMAIN of parabolas is all real numbers…unless the parabola looks like this
and has endpoint(s)
8
We say the domain is restricted, therefore it is no longer all real numbers
Find the domain of the graph below
Domain:
9
1,2
x
y
-1 < x < 2
Find the domain of the graph below
Domain:
10
2,2-2 < x < 2
x
y
Find the domain of the graph below
Domain:
11
2,
x
y
2 x
2( ) 2 4 1f x x x
Vertex:
Y-intercept:
Axis of symmetry:
One more point:
Domain:
Range:
Max or Min?
Graph the quadratic using the axis of symmetry and vertex.
1x
1,3
0,1
3, 5
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.
1x
0,1
1,4
minimum
All real numbersy ≥ 0
13
2( ) ( 1)f x x (-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.
3
2 1x
2bxa
32
x
3 5,2 4
0, 1
1,1
maximum
All real numbers
14
2( ) 3 1f x x x
54
y Extrema: y = 5/4
Stretch VS. Shrink Compare the following graphs and equations:
2y x
23y x21
3y x
What is the difference between these two
graphs when compared to the parent function?
*note: rubber bandVertical stretch Vertical shrink
Look at a couple more… 22 1 2y x 22 2 4
5y x
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 stretch When a is less than 1, we call that a vertical shrink
State whether the graph shows a vertical stretch or vertical shrink
Shrink…so |a| < 1
Stretch…so |a| > 1
Stretch…so |a| > 1
18
Intervals of increase and decrease
To determine the intervals of increase and decrease, you must “read” the graph from left to right
What are these lines doing from left to
right?
19
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 this parabola doing
on the left side of the vertex?
Going downhill
What is this parabola doing
on the right side of the
vertex?Going uphill
Interval of decrease , 3 Interval of increase 3,
20
One more…
What is this parabola doing on the left side of the vertex?
Going uphill
What is this parabola doing
on the right side of the
vertex?Going downhill
Interval of decrease 2, Interval of increase , 2
21
Graph each quadratic function and determine the interval of increase and decrease
3,4
Interval of decrease 3,
Interval of increase ,3
y = -2x² + 12x - 14
22
1,2
Interval of decrease , 1
Interval of increase 1,
Graph each quadratic function and determine the interval of increase and decrease
y = x² + 2x + 3
23
3 11,2 2
Interval of decrease 3,2
Interval of increase 3 ,2
23. ( ) 2 6 1f x x x 6
2 2x
2bxa
23 3 3( ) 2 6 12 2 2
f
3 11( )2 2
f
32
x
Graph each quadratic function and determine the interval of increase and decrease
24
Determine if the given interval is an interval of increase or decrease
4. 4 1x 5. 2 5x decrease increase
25
Determine if the given interval is an interval of increase or decrease
6. 5 9x 7. 5 3x - increase increase
26
Assignment: Day 2 Handout
