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.