8
advanced-math

The function y=12x2y = \frac{1}{2}x^2 is:

A

Wider than y=x2y = x^2

B

Narrower than y=x2y = x^2

C

Shifted right 0.5

D

Reflected

Correct Answer: A

Choice A is the correct answer.

  1. The coefficient is a=1/2a = 1/2.
  2. Since 0<a<10 < |a| < 1, the graph is vertically compressed (squashed) towards the x-axis.
  3. This makes the parabola appear wider than the standard y=x2y=x^2.

Choice B is incorrect because that requires a>1|a| > 1. Choice C is incorrect because there is no horizontal shift. Choice D is incorrect because aa is positive.