Question
Question 1 of 10
How would you describe the difference between the graphs of
and
?
A.
is a reflection of
over the
-axis.
B.
is a reflection of
over the line
.
C.
is a reflection of
over the x-axis.
D.
is a reflection of
over the line
.
How would you describe the difference between the graphs of
and
A.
B.
C.
D.
Ask by Wood Ball. in the United States
Nov 07,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
C.
is a reflection of
over the x-axis.
Solution
To analyze the functions
and
, we can observe their characteristics:
- The function
is a parabola that opens upwards, with its vertex at the origin (0,0). - The function
is a parabola that opens downwards, also with its vertex at the origin (0,0).
The key difference between these two functions is that
has a negative coefficient, which means it is a reflection of
across the x-axis.
Thus, the correct answer is:
C.
is a reflection of
over the x-axis.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
The graphs of
and
offer a fantastic illustration of symmetry! The function
opens upwards, resembling a smiling face, while
flips it upside down, creating a frown. They are equal in width but opposite in direction, showing how a negative sign transforms the shape instantly.
When you take a closer look at their equations, you can find that
is indeed just a reflection of
over the x-axis. This realization reveals the beauty of quadratic functions and how transformations can alter their appearances, giving you another reason to love the world of graphs!