The problem in the image asks for calculating the values of $f(x)$ for specific inputs, where the function is given as:

$f(x) = 4x^2 + 4x + 5$

You need to calculate $f(x)$ for $x = -2, -1, 0, 1, 2$. Let's go through each one step by step:

1. $f(-2)$: $f(-2) = 4(-2)^2 + 4(-2) + 5 = 4(4) - 8 + 5 = 16 - 8 + 5 = 13$ So, $f(-2) = 13$.

2. $f(-1)$: $f(-1) = 4(-1)^2 + 4(-1) + 5 = 4(1) - 4 + 5 = 4 - 4 + 5 = 5$ So, $f(-1) = 5$.

3. $f(0)$: $f(0) = 4(0)^2 + 4(0) + 5 = 0 + 0 + 5 = 5$ So, $f(0) = 5$.

4. $f(1)$: $f(1) = 4(1)^2 + 4(1) + 5 = 4(1) + 4 + 5 = 4 + 4 + 5 = 13$ So, $f(1) = 13$.

5. $f(2)$: $f(2) = 4(2)^2 + 4(2) + 5 = 4(4) + 8 + 5 = 16 + 8 + 5 = 29$ So, $f(2) = 29$.

Final Results:

• $f(-2) = 13$
• $f(-1) = 5$
• $f(0) = 5$
• $f(1) = 13$
• $f(2) = 29$

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

1. What is the vertex of the quadratic function $f(x) = 4x^2 + 4x + 5$?
2. How does the value of $f(x)$ change as $x$ increases?
3. How would you solve $f(x) = 0$ for this quadratic function?
4. How can you find the axis of symmetry for the function $f(x) = 4x^2 + 4x + 5$?
5. What is the domain and range of $f(x) = 4x^2 + 4x + 5$?

Tip: Always substitute values carefully when evaluating a function, and make sure to handle negative numbers correctly.