Question

match the graph with its function y=2x²

Explanation:

Step1: Identify base function properties

The parent function is $y=x^2$, a parabola opening upward with vertex at $(0,0)$. For $y=2x^2$, the coefficient $2>1$, so the parabola is narrower than $y=x^2$.

Step2: Test key points

Calculate $y$ for $x=1$: $y=2(1)^2=2$. For $x=2$: $y=2(2)^2=8$. These points confirm a narrow upward-opening parabola with vertex at the origin.

Step3: Match to correct graph

Compare with options: Graph C is a narrow upward-opening parabola passing through $(1,2)$ and $(2,8)$, matching $y=2x^2$.

Answer:

C. <The graph labeled C, a narrow upward-opening parabola with vertex at (0,0)>