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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.

Given f(x) = 2x^2 + 5x + 3, at what point does the graph intersect the y-axis?

Discover how to find the y-intercept of the quadratic function f(x) = 2x^2 + 5x + 3. By substituting x = 0, we identify the point where the graph intersects the y-axis, a key concept in algebra for students in Grades 8-10.

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