Match the Quadratic Function y = 2x² + 3 to Its Correct Graph

To solve this problem, we need to match the quadratic function $y = 2x^2 + 3$ with one of the graph choices.

First, identify the characteristics of the parabola:

• The standard form of the function is $y = 2x^2 + 3$, which is already in vertex form for vertical shift.
• The parabola opens upwards since the coefficient of $x^2$ is positive ($a = 2$).
• The vertex of the parabola is at $(0, 3)$, not subject to any horizontal shifts. The only transformation from $y = x^2$ is the vertical shift by 3 units up.

Now, assess the graph choices:

• Look for a parabola that is centered on the vertical axis (origin along the x-axis) and opens upwards.
• Among the provided graphs, the one depicting an upright parabola with vertex at $(0, 3)$ should correspond to our function.

The correct choice is graph 3, as it aligns with our function's characteristics: opening upwards, vertex located at $(0, 3)$.

Therefore, the solution to the problem is graph 3.