Answer:
Option B is correct.
Step-by-step explanation:
Given: \(y=3x^2+2\)
We need to choose correct graph whose wider than given graph.
For wider, we check the coefficient of x².
For function y=ax²
If a>1 then compressed
If a<1 then wider
We will compare the coefficient of x² for each option.
Option A: \(y=3x^2+2\)
\(3x^2+2\rightarrow 3x^2+2\) Identical graph.
Option B: \(y=0.5x^2+1\)
\(3x^2+2\rightarrow 0.5x^2+1\)
3>0.5, Graph becomes wider than older one.
Option C: \(y=3x^2+2\)
\(3x^2+2\rightarrow 4x^2+1\)
3<4, Graph thinner than original graph.
Option D: \(y=3x^2+2\)
\(3x^2+2\rightarrow 4x^2+1\)
3<4, Graph is thinner than original graph.
Hence, Option B is correct. (Please see attachment for graph)
