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.
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
Related questions
Question
100%

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 is on the parabola, then is also on the parabola for every point . Now, the points and 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.
Step by step
Solved in 2 steps

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

