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.