https://file.aiquickdraw.com/mathbot/file/17278661721099s0hww9b.jpg

The quadratic function provided is:

\[
y = 0.8(x - 3)^2 + 1.5
\]

This is in vertex form, \( y = a(x - h)^2 + k \), where \((h, k)\) represents the vertex of the parabola. Comparing it to the given equation:

- \( h = 3 \)
- \( k = 1.5 \)

Thus, the vertex of the parabola is \( (3, 1.5) \).

So, the correct answer to fill in the blank is:

**3**

Would you like further details or have any questions?

Here are 5 follow-up questions to expand your understanding:
1. What does the coefficient \( 0.8 \) in the equation represent in terms of the graph's shape?
2. How does changing \( h \) affect the horizontal position of the vertex?
3. What happens if the sign of the coefficient \( a \) is negative?
4. How do you find the axis of symmetry of this parabola?
5. What is the significance of the vertex in real-world applications of quadratic functions?

**Tip**: The vertex form of a quadratic function is useful for quickly identifying the vertex and understanding the direction and width of the parabola.

Consider the quadratic function y = 0.8(x - 3)^2 + 1.5. This parabola opens up with its vertex at ( ____, 1.5).

Learn how to determine the vertex of the quadratic function y = 0.8(x - 3)^2 + 1.5. This problem introduces key concepts such as vertex form and the behavior of parabolas, suitable for students in Grades 9-11.

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