Look at the graph of the function (x) below. Which statements regarding the parabola's axis of symmetry are true? Select the three correct statements. A B с D -10-9-8-7-6-5-4 y 19 172 15 13- 114 9 74 => 1.9 -3 5 -7+ -9. -11- 134 as The vertex is on the axis of symmetry. The x-axis is the axis of symmetry. The axis of symmetry is the line x=0. 56 9 10 If the point (a, b) is a point on the parabola, then the point (a, b) is also a point on the parabola, because it is a reflection over the axis of symmetry.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Look at the graph of the function f(x) below.
Which statements regarding the parabola's axis of symmetry are true?
Select the three correct statements.
A
B
C
D
-10-9-8-7-6-5-4-3-2
Y
19
174
15
13
11-
9-
74
-1
5-
3
0
-3
5
-7-
-24
11-
134
15
4174
The vertex is on the axis of symmetry.
The x-axis is the axis of symmetry.
The axis of symmetry is the line x = 0.
5 6 7 8 9 10
X
If the point (a, b) is a point on the parabola, then the point (-a, b) is also a point on
the parabola. because it is a reflection over the axis of symmetry.
Transcribed Image Text:Look at the graph of the function f(x) below. Which statements regarding the parabola's axis of symmetry are true? Select the three correct statements. A B C D -10-9-8-7-6-5-4-3-2 Y 19 174 15 13 11- 9- 74 -1 5- 3 0 -3 5 -7- -24 11- 134 15 4174 The vertex is on the axis of symmetry. The x-axis is the axis of symmetry. The axis of symmetry is the line x = 0. 5 6 7 8 9 10 X If the point (a, b) is a point on the parabola, then the point (-a, b) is also a point on the parabola. because it is a reflection over the axis of symmetry.
Expert Solution
Step 1

From the graph we see that if (a, b) is on the parabola, then (-a, b) is also on the parabola for every point (a, b). Now, the points (a, b) and (-a, b) are the point of reflection of each other about y-axis. So, the y-axis is the axis of symmetry.

Therefore, the option B is false and the option D is true.

The equation of y-axis is x=0 and y-axis is the axis of symmetry. So, the axis of symmetry is the line x=0.

Therefore, the option C is true.

Again, the vertex of the given parabola f(x) is (0, 1), which is on the y-axis and y-axis is the axis of symmetry. So, the vertex of the parabola is on the axis of symmetry.

Therefore, the option A is true.

 

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