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We are given two functions:

\[
f(x) = -4x^2 - 3 \quad \text{and} \quad g(x) = -2x + 2
\]

We need to find \( f(4) \) and \( g(7) \).

### Step 1: Find \( f(4) \)

Substitute \( x = 4 \) into the equation for \( f(x) \):

\[
f(4) = -4(4)^2 - 3 = -4(16) - 3 = -64 - 3 = -67
\]

So, \( f(4) = -67 \).

### Step 2: Find \( g(7) \)

Substitute \( x = 7 \) into the equation for \( g(x) \):

\[
g(7) = -2(7) + 2 = -14 + 2 = -12
\]

So, \( g(7) = -12 \).

### Final Answers:

- \( f(4) = -67 \)
- \( g(7) = -12 \)

Would you like further details or have any other questions? Here are 5 related questions you might find interesting:

1. What happens to the values of \( f(x) \) and \( g(x) \) as \( x \) increases indefinitely?
2. What are the vertex and intercepts of the quadratic function \( f(x) = -4x^2 - 3 \)?
3. How does the slope of the linear function \( g(x) = -2x + 2 \) affect its graph?
4. Can you find the intersection points of \( f(x) \) and \( g(x) \)?
5. How would you approach solving for \( x \) if \( f(x) = 0 \)?

Tip: For quadratic functions like \( f(x) = -4x^2 - 3 \), the negative coefficient of \( x^2 \) indicates that the parabola opens downward.

Find f(4) and g(7) for the functions f(x) = -4x^2 - 3 and g(x) = -2x + 2. Simplify your answers as much as possible.

Find the values of f(4) and g(7) by solving the quadratic function f(x) = -4x^2 - 3 and the linear function g(x) = -2x + 2. This exercise covers algebraic concepts and function evaluation suitable for Grades 7-9.

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