Find minus, 5, h, of, minus, 6, plus, 4, g, of, minus, 1−5h(−6)+4g(−1) in simplified form.
x
y
h(x)
g, of, x, equals, minus, x, squared, minus, 5, x, minus, 1g(x)=−x
2
−5x−1

xx	f, of, xf(x)
44	55
77	66
00	minus, 9−9
minus, 8−8	44

Let's break down the problem you provided step by step. We are asked to find the value of:

\[
-5h(-6) + 4g(-1)
\]

We are also given the following information:

1. A table of values for \( f(x) \) (though it may not be directly relevant to \( h(x) \) and \( g(x) \) unless specified):
   - \( f(4) = 5 \)
   - \( f(7) = 6 \)
   - \( f(0) = -9 \)
   - \( f(-8) = 4 \)

2. The function \( g(x) \) is defined as:
\[
g(x) = -x^2 - 5x - 1
\]

However, the function \( h(x) \) is not directly defined. To proceed, let's assume \( h(x) \) is related to \( f(x) \), and we can interpret it using the table, where values of \( h(x) \) correspond to values of \( f(x) \).

### Step 1: Evaluate \( h(-6) \)
Since \( h(x) \) isn't explicitly defined, if \( h(x) = f(x) \), we check if \( f(-6) \) is in the table, but it's not provided. Without more details, we can't evaluate \( h(-6) \) definitively.

### Step 2: Evaluate \( g(-1) \)
We can evaluate \( g(-1) \) using the given formula for \( g(x) \):
\[
g(-1) = -(-1)^2 - 5(-1) - 1
\]
Simplify:
\[
g(-1) = -1 + 5 - 1 = 3
\]

### Step 3: Substitute the values back into the expression
We have:
\[
-5h(-6) + 4g(-1) = -5h(-6) + 4(3)
\]
This simplifies to:
\[
-5h(-6) + 12
\]

Since we don't have a clear definition for \( h(-6) \), we can't simplify this expression further. If \( h(x) = f(x) \), and \( f(-6) \) is missing from the provided table, we'd need that value to fully simplify.

Would you like further clarification or more details on any part of the problem?

---

Here are 5 related questions to think about:

1. What is the role of function \( h(x) \) in this problem?
2. How would you define a function based on a table of values?
3. What happens when a function's values aren't given for certain inputs?
4. Can we infer more about \( f(x) \) from the table or create an equation for it?
5. How do you graph quadratic functions like \( g(x) = -x^2 - 5x - 1 \)?

**Tip:** Always make sure that all functions used in a problem are clearly defined before attempting to solve it.

Find minus, 5, h, of, minus, 6, plus, 4, g, of, minus, 1−5h(−6)+4g(−1) in simplified form. x y h(x) g(x) equals minus x squared minus 5x minus 1.

Learn how to simplify the expression -5h(-6) + 4g(-1), where g(x) is a quadratic function, and h(x) is partially defined through given values. Suitable for students in Grades 9-11, this problem explores algebraic manipulation and function evaluation.

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