Question

How does the graph of $-y=x^{2}$ compare to the graph of $y=x^{2} ?$ Explain your answer.

Name: Problem 33, Chapter 8: Intermediate Algebra
Uploaded: 2022-03-31T21:06:35-08:00
Duration: 55 s
Channel: Victor Salazar
Description: How does the graph of -y=x^2 compare to the graph of y=x^2 ? Explain your answer.

   How does the graph of $-y=x^{2}$ compare to the graph of $y=x^{2} ?$ Explain your answer.

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 8, Problem 33

Instant Answer

Solved by Expert Victor Salazar

03/31/2022

Step 1

This is a standard parabola that opens upwards with its vertex at the origin (0,0). The graph is symmetric with respect to the y-axis. Show more…

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How does the graph of $-y=x^{2}$ compare to the graph of $y=x^{2} ?$ Explain your answer.

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Key Concepts

Vertical Reflection

A vertical reflection occurs when the outputs (y-values) of a function are multiplied by -1, causing every point on a graph to be flipped over the x-axis. This transformation means that if a point (x, y) is on the original graph, the transformed graph will contain the point (x, -y).

Graph Transformation

Graph transformations refer to operations that modify the appearance of a graph, such as translations, scaling, and reflections. Multiplying by -1 in the output results in a vertical reflection, changing the direction of the graph’s opening without affecting its shape.

Quadratic Function

A quadratic function, typically written in the form y = ax², produces a parabolic graph. Changing the sign of the function flips the parabola vertically, so a graph that opens upward will open downward. This is essential in understanding how graphs of quadratic equations can be manipulated through algebraic modifications.

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