Lesson 4.3 Math Lab: Assess Your Understanding, pages...
Transcript of Lesson 4.3 Math Lab: Assess Your Understanding, pages...
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94.3 Math Lab: Transforming the Graph of y = x2—Solutions©P DO NOT COPY.
Lesson 4.3 Math Lab: Assess Your Understanding, pages 269–271
1. Complete this table for the graph of each function.
Function Direction ofopening
Vertex Axis ofsymmetry
Congruentto y � x2?
y = x2
y = (x - 7)2
y = (x + 8)2
y = x2+ 7
y = x2- 8
y = 7x2
y = -7x2
up (0, 0) x = 0 yes
up (7, 0) yes
up (�8, 0) yes
up (0, 7) yes
up (0, �8) yes
up (0, 0) no
down (0, 0) no x � 0
x � 0
x � 0
x � 0
x � �8
x � 7
04_ch04_pre-calculas11_wncp_solution.qxd 6/3/11 11:46 AM Page 9
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10 4.3 Math Lab: Transforming the Graph of y = x2—Solutions DO NOT COPY. ©P
2. On grid paper, graph . Graph each quadratic functionwithout using a table of values or a graphing calculator.Explain your strategy each time.
a) y = x2- 4y = x2
+ 5
y = x2
4
6
8
x
2
�2
�4
2 4 60�2�4�6
yy � x2 � 5
y � x2 � 4y � x2
c) y =12x2y = 2x2
b) y = (x - 5)2y = (x + 3)2
4
8
x
2
�2
2 4 6 80�2�4�6
y
y � x2
y � (x � 5)2y � (x � 3)2
4
6
8
x
2
�2
2 4 60�2�4�6
yy � x2y � 2x2
y � x212
I translate the graph of 5 units up to get the graph of . I translate the graph of 4 units down to get the graph of
.y � x2 � 4
y � x2y � x2 � 5
y � x2
I translate the graph of 3 units left to get the graph of
. I translate the graph of 5 units right to get the graph of
.y � (x � 5)2
y � x2y � (x � 3)2
y � x2
I double the y-coordinate of each point on the graph of
to get the graph of . I halve the y-coordinate of each point on the graph of to
get the graph of y �12 x 2.
y � x2
y � 2x2y � x2
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114.3 Math Lab: Transforming the Graph of y = x2—Solutions©P DO NOT COPY.
4. What happens to the axis of symmetry of the parabola in each case?
a) The graph of is translated 5 units left.
b) The graph of is translated 5 units down.y = x2
y = x2
3. The graph of is translated as described below. Withoutgraphing, write the equation of the graph in its new position.
a) a translation of 30 units left b) a translation of 250 units up
c) a translation of 21 units right d) a translation of 83 units down
y = x2
d) y = -14x2y = -4x2
4
6
8
x
y
2
�2
�4
�6
�8
2 4 60�2�4�6
y � x2
y � �4x2
y � � x214
The axis of symmetry moves 5 units left.
The axis of symmetry does not move.
y � x2 � 250y � (x � 30)2
y � x2 � 83y � (x � 21)2
I multiply the y-coordinate of each point on the graph of
by 4, then reflect the point in the x-axis to get the graph of . I divide the y-coordinate of each point on the graph of by 4, then reflect the point in the x-axis
to get the graph of .y � �14x2
y � x2
y � �4x2
y � x2
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