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To find the value of \( a \) such that the point \( (1, 4) \) lies on the graph of the function \( f(x) = ax^2 + 2 \), we need to use the fact that the point \( (1, 4) \) satisfies the function. This means that when \( x = 1 \), \( f(x) = 4 \).

### Steps:

1. The function is \( f(x) = ax^2 + 2 \).
2. Substitute \( x = 1 \) and \( f(1) = 4 \) into the function:
   \[
   4 = a(1)^2 + 2
   \]
3. Simplify the equation:
   \[
   4 = a + 2
   \]
4. Solve for \( a \):
   \[
   a = 4 - 2 = 2
   \]

Thus, the value of \( a \) is \( \boxed{2} \).

Would you like any more details or further explanation? Here are some related questions:

1. How do we verify if a point lies on a graph?
2. What happens to the graph when we change the value of \( a \) in the quadratic equation?
3. Can we find the vertex of the function \( f(x) = ax^2 + 2 \)?
4. How do we find the axis of symmetry for a quadratic function?
5. How can we determine if a quadratic function opens upwards or downwards?

**Tip**: For quadratic functions, the sign of \( a \) in \( f(x) = ax^2 + bx + c \) determines whether the parabola opens upwards (\( a > 0 \)) or downwards (\( a < 0 \)).

Find a so that the point (1,4) is on the graph of f(x) = ax^2 + 2.

In this problem, we determine the value of 'a' in the quadratic function f(x) = ax^2 + 2 such that the point (1,4) lies on the graph. This solution involves basic algebraic manipulation and is suitable for students in Grades 7-9.

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