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The problem asks for the equation of a quadratic graph with a given maximum point at \( (2, 5) \).

### Step 1: Use the vertex form of a quadratic equation.
The quadratic equation can be written in vertex form as:
\[
y = a(x - h)^2 + k
\]
where \( (h, k) \) is the vertex of the parabola. In this case, the vertex is \( (2, 5) \), so we substitute \( h = 2 \) and \( k = 5 \):
\[
y = a(x - 2)^2 + 5
\]
Since the graph has a maximum point, the parabola opens downward, which means \( a \) must be negative.

### Step 2: Determine the value of \( a \).
To find the specific value of \( a \), we would need one more point on the graph. However, since no additional point is given, we can leave the equation in the general form with \( a \) being negative:
\[
y = a(x - 2)^2 + 5
\]
If an additional point were provided, you could plug that point into the equation to solve for \( a \).

### Final equation:
Without more information, the equation in vertex form is:
\[
y = a(x - 2)^2 + 5
\]
where \( a \) is a negative constant.

Would you like to provide another point to determine \( a \), or do you have any other questions about this problem?

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Here are 5 related questions for further practice:
1. How do you find the equation of a quadratic graph if given the vertex and one more point?
2. What is the significance of the value of \( a \) in the vertex form of a quadratic equation?
3. How can you convert a quadratic equation from vertex form to standard form?
4. If the maximum point were at \( (3, 7) \), how would the equation change?
5. How does the vertex form of a quadratic equation help in graphing the parabola?

### Tip:
Remember that the sign of \( a \) determines whether the parabola opens upwards (positive \( a \)) or downwards (negative \( a \)).

A quadratic graph has maximum point (2, 5). Find an equation for the graph.

Find the equation of a quadratic graph with a maximum point at (2, 5). Learn how to use the vertex form of a quadratic equation to determine the equation of the parabola. Suitable for high school students in Grades 9-12.

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