Question: Express the interval shown on the number line in interval notation.
Given f(x) = -x^2 + 9x - 17, find f(-5)
1. **Problem 1: Express the interval shown on the number line in interval notation.**
The number line shows a green ray extending leftward toward negative infinity with a closed green dot at 0.
2. **Interval notation rules:**
- A closed dot means the endpoint is included, so use a square bracket $[$ or $]$.
- An open ray toward negative infinity means the interval extends to $-\infty$.
3. **Interval notation for the ray:**
$$(-\infty, 0]$$
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4. **Problem 2: Given $f(x) = -x^2 + 9x - 17$, find $f(-5)$.**
5. **Substitute $x = -5$ into the function:**
$$f(-5) = -(-5)^2 + 9(-5) - 17$$
6. **Calculate step-by-step:**
$$(-5)^2 = 25$$
$$f(-5) = -25 + (-45) - 17$$
7. **Simplify:**
$$-25 - 45 - 17 = -87$$
8. **Final answer:**
$$f(-5) = -87$$