The problem is asking where the graph of the function $f(x) = 2x^2 + 5x + 3$ intersects the $y$-axis.

To find where a graph intersects the $y$-axis, we substitute $x = 0$ into the equation of the function, since the $y$-axis corresponds to $x = 0$.

Given: $f(x) = 2x^2 + 5x + 3$ Substitute $x = 0$: $f(0) = 2(0)^2 + 5(0) + 3 = 3$ Thus, the point where the function intersects the $y$-axis is $(0, 3)$.

The correct answer is $\text{A}$.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you determine where a function intersects the $x$-axis?
2. Can a quadratic function intersect the $y$-axis more than once?
3. What is the significance of the vertex in the graph of a quadratic function?
4. How do the coefficients of a quadratic equation affect the graph's shape and direction?
5. How can we find the roots of $f(x) = 2x^2 + 5x + 3$?

Tip: The y-intercept is always found by setting $x = 0$ in any function.