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### Problem Breakdown:
The problem has two parts:

**(a)** The x-intercepts of a particular equation are \( x = 2 \) and \( x = 5 \). You need to suggest a possible equation.

**(b)** If the y-intercept in part (a) is \( (0, 4) \), you need to find the exact equation.

### Solution:

**(a)**

Since the x-intercepts of the equation are \( x = 2 \) and \( x = 5 \), the equation can be represented as:
\[
y = a(x - 2)(x - 5)
\]
Here, \( a \) is a constant that can be determined using additional information.

**(b)**

Given that the y-intercept is \( (0, 4) \), we substitute \( x = 0 \) and \( y = 4 \) into the equation:
\[
4 = a(0 - 2)(0 - 5)
\]
\[
4 = a(2)(5)
\]
\[
4 = 10a
\]
\[
a = \frac{4}{10} = \frac{2}{5}
\]

So, the exact equation is:
\[
y = \frac{2}{5}(x - 2)(x - 5)
\]

Would you like further details on any step? Here are some related questions that might interest you:

1. What does the value of \( a \) signify in a quadratic equation?
2. How can the vertex form of a quadratic equation be derived from its factored form?
3. What are the implications of the x-intercepts in the graph of a quadratic equation?
4. How do you find the axis of symmetry for a quadratic equation?
5. What is the importance of the discriminant in solving quadratic equations?

**Tip:** The constant \( a \) in a quadratic equation \( y = a(x - r_1)(x - r_2) \) determines the direction and the width of the parabola's opening.

Explore how to solve a quadratic equation given specific x-intercepts and a y-intercept. This problem involves determining the equation using intercepts and substitution, crucial for understanding quadratic functions. Suitable for high school students.

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