3
advanced-math

Describe the transformation of y=−x2y = -x^2 compared to y=x2y = x^2.

A

Reflected over the x-axis

B

Reflected over the y-axis

C

Shifted down 1 unit

D

Made narrower

Correct Answer: A

Choice A is the correct answer. Multiplying the output of the function by -1 (i.e., y=−f(x)y = -f(x)) reflects the graph across the x-axis.

  1. y=x2y = x^2 opens upward.
  2. y=−x2y = -x^2 opens downward.

Choice B is incorrect because y=(−x)2=x2y = (-x)^2 = x^2 is the same graph (symmetric over y-axis). Choice C is incorrect because that would be x2−1x^2 - 1. Choice D is incorrect because the coefficient magnitude is still 1.

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Set 7: Quadratic Equations and Functions 7