Question

1. $f(x)=x^2 - 10x + 25$ (text cut off)
2. $f(x)=|x - 3| - 4$; find $f(-8)$
3. $f(x)=-x^2 - 4x + 2$; find $f(-4)$
4. $f(x)=-3|x + 4| + 1$; find $f(-5)$

Explanation:

Problem 5: \( f(x) = |x - 3| - 4 \); Find \( f(-8) \)

Step1: Substitute \( x = -8 \) into the function

Substitute \( x = -8 \) into \( f(x) = |x - 3| - 4 \), we get \( f(-8) = |-8 - 3| - 4 \).

Step2: Calculate the absolute value

First, calculate the expression inside the absolute value: \( -8 - 3 = -11 \). Then, the absolute value of \( -11 \) is \( |-11| = 11 \).

Step3: Perform the subtraction

Now, subtract 4 from 11: \( 11 - 4 = 7 \).

Step1: Substitute \( x = -4 \) into the function

Substitute \( x = -4 \) into \( f(x) = -x^2 - 4x + 2 \), we get \( f(-4) = -(-4)^2 - 4(-4) + 2 \).

Step2: Calculate the powers and multiplications

First, calculate \( (-4)^2 = 16 \), so \( -(-4)^2 = -16 \). Then, calculate \( -4(-4) = 16 \).

Step3: Perform the addition and subtraction

Now, substitute these values back: \( -16 + 16 + 2 = 0 + 2 = 2 \).

Step1: Substitute \( x = -5 \) into the function

Substitute \( x = -5 \) into \( f(x) = -3|x + 4| + 1 \), we get \( f(-5) = -3|-5 + 4| + 1 \).

Step2: Calculate the absolute value

First, calculate the expression inside the absolute value: \( -5 + 4 = -1 \). Then, the absolute value of \( -1 \) is \( |-1| = 1 \).

Step3: Perform the multiplication and addition

Multiply \( -3 \) by 1: \( -3 \times 1 = -3 \). Then, add 1: \( -3 + 1 = -2 \).

Answer:

\( f(-8) = 7 \)

Problem 7: \( f(x) = -x^2 - 4x + 2 \); Find \( f(-4) \)