We are analyzing the quadratic function $y = -1.5(x+20)^2$. Here's the breakdown:

1. Vertex:

The function is in vertex form: $y = a(x-h)^2 + k$. Here:

• $h = -20$ (the opposite sign of the value inside the parentheses),
• $k = 0$ (constant outside the parentheses).

Thus, the vertex is $(-20, 0)$.

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2. Axis of Symmetry:

The axis of symmetry is the vertical line that passes through the vertex: $x = -20$

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3. Maximum or Minimum Value:

Since the coefficient of the squared term ($a = -1.5$) is negative, the parabola opens downward, and the vertex represents the maximum point.

• Maximum value: $y = 0$ (the $y$-coordinate of the vertex).

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4. Domain:

For any quadratic function, the domain is all real numbers: $\text{Domain: } (-\infty, \infty)$

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5. Range:

Because the parabola opens downward and its maximum value is $y = 0$, the range includes all values less than or equal to 0: $\text{Range: } (-\infty, 0]$

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Final Answer:

1. Vertex: $(-20, 0)$
2. Axis of Symmetry: $x = -20$
3. Maximum Value: $y = 0$
4. Domain: $(-\infty, \infty)$
5. Range: $(-\infty, 0]$

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Would you like further explanations or graphs?
Here are 5 questions you might explore next:

1. How do you graph $y = -1.5(x+20)^2$?
2. What is the significance of the negative leading coefficient?
3. How would the function