D) If \( f(x)=(x-2)^{2} \); find the following. \( \begin{array}{ll}\text { 1) } 4 f(1) \times 6 f(0)=\square & \text { 2) }-8 f(2)+3 f(4)= \\ \text { 3) }-7 f(7)+f(-8)= \\ \text { What is the value of } f(-3) \text {, if } f(x)=10 x^{2}+8 ? & \text { i) } \frac{-3 f(-1)}{f(3)} \\ \text { i) } 9 \text { if }-88 & \text { lii) } 96\end{array} \)

Let's tackle each part of the problem step by step. --- **Given:** \[ f(x) = (x - 2)^2 \] --- ### **1) Calculate \( 4f(1) \times 6f(0) \)** **Step 1: Compute \( f(1) \)** \[ f(1) = (1 - 2)^2 = (-1)^2 = 1 \] **Step 2: Compute \( f(0) \)** \[ f(0) = (0 - 2)^2 = (-2)^2 = 4 \] **Step 3: Calculate the expression** \[ 4f(1) \times 6f(0) = 4 \times 1 \times 6 \times 4 = 4 \times 1 = 4 \\ 4 \times 6 = 24 \\ 24 \times 4 = 96 \] **Answer:** \( 96 \) --- ### **2) Calculate \( -8f(2) + 3f(4) \)** **Step 1: Compute \( f(2) \)** \[ f(2) = (2 - 2)^2 = 0^2 = 0 \] **Step 2: Compute \( f(4) \)** \[ f(4) = (4 - 2)^2 = 2^2 = 4 \] **Step 3: Calculate the expression** \[ -8f(2) + 3f(4) = -8 \times 0 + 3 \times 4 = 0 + 12 = 12 \] **Answer:** \( 12 \) --- ### **3) Calculate \( -7f(7) + f(-8) \)** **Step 1: Compute \( f(7) \)** \[ f(7) = (7 - 2)^2 = 5^2 = 25 \] **Step 2: Compute \( f(-8) \)** \[ f(-8) = (-8 - 2)^2 = (-10)^2 = 100 \] **Step 3: Calculate the expression** \[ -7f(7) + f(-8) = -7 \times 25 + 100 = -175 + 100 = -75 \] **Answer:** \( -75 \) --- ### **4) Find \( f(-3) \) when \( f(x) = 10x^2 + 8 \)** **Given Function:** \[ f(x) = 10x^2 + 8 \] **Compute \( f(-3) \):** \[ f(-3) = 10 \times (-3)^2 + 8 = 10 \times 9 + 8 = 90 + 8 = 98 \] **Final Answer:** \( f(-3) = 98 \) --- **Summary of Answers:** 1. \( 4f(1) \times 6f(0) = 96 \) 2. \( -8f(2) + 3f(4) = 12 \) 3. \( -7f(7) + f(-8) = -75 \) 4. \( f(-3) = 98 \) when \( f(x) = 10x^2 + 8 \)