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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 .

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:
  1. The function is a parabola that opens upwards, with its vertex at the origin (0,0).
  2. 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.

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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!

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