Instructions:
1
.
Submissions can by typed or hand
-
written.
2
.
Organise your answers in the order in which the questions are asked below.
3
.
Provide full working
/
justification for your

Question

Instructions: 
1
.
 ﻿Submissions can by typed or hand
-
written. 
2
.
 ﻿Organise your answers in the order in which the questions are asked below. 
3
.
 ﻿Provide full working
/
justification for your answers. You cannot use Matlab 
(
or similar
)
 ﻿to justify your answers unless explicit instructed to the contrary. Your answers must be explained and justified clearly in a manner that can be easily understood. 
4
.
 ﻿Submit your assignment via the Canvas submission folder. 
5
.
 ﻿Although it is acceptable for students to discuss assignment questions it is expected that any work submitted is that of the submitting student 
(
i
.
e
.
 ﻿do not copy each others work
)
.
 ﻿If it is suspected that your submission has been copied from another source or another student then you will be referred to the Associate Dean 
(
Teaching and Learning
)
 ﻿of the School of Science for possible punishment via an academic penalty. If you are negligent enough to allow another student the opportunity to copy your work then you will be deemed an accessory to academic misconduct and may also be penalised for your part in the fraud.

Provide the complete solution in structural manner from start to end, i ne

VIPSolutions · Accepted Answer

# Assignment Solution

---

## 1. Complete Solution with All Calculations

### **Question 1**  
*(Assuming an example question as the original question is not provided. Replace this with the actual question as needed.)*

**Given:**  
Let $ f(x) = 2x^2 + 3x - 5 $.  
Find the values of $ f(2) $ and $ f(-1) $.

#### **Solution Steps**

**Step 1: Evaluate $ f(2) $**

$$
f(2) = 2(2)^2 + 3(2) - 5
$$
$$
= 2 \times 4 + 6 - 5
$$
$$
= 8 + 6 - 5
$$
$$
= 14 - 5
$$
$$
= 9
$$

**Step 2: Evaluate $ f(-1) $**

$$
f(-1) = 2(-1)^2 + 3(-1) - 5
$$
$$
= 2 \times 1 - 3 - 5
$$
$$
= 2 - 3 - 5
$$
$$
= -1 - 5
$$
$$
= -6
$$

---

## 2. Explanation of Each and Every Part

### **Step 1 Explanation: Evaluating $ f(2) $**

- Substitute $ x = 2 $ into the function.
- Calculate $ (2)^2 = 4 $.
- Multiply by 2 to get 8.
- Multiply 3 by 2 to get 6.
- Add all terms: $ 8 + 6 - 5 $.
- Add 8 and 6 to get 14.
- Subtract 5 to obtain the final result of 9.

### **Step 2 Explanation: Evaluating $ f(-1) $**

- Substitute $ x = -1 $ into the function.
- Calculate $ (-1)^2 = 1 $.
- Multiply by 2 to get 2.
- Multiply 3 by $-1$ to get $-3$.
- Add all terms: $ 2 - 3 - 5 $.
- Combine 2 and $-3$ to get $-1$.
- Subtract 5 to obtain the final result of $-6$.

---

## 3. Final Conclusion Statement

The function $ f(x) = 2x^2 + 3x - 5 $ yields $ f(2) = 9 $ and $ f(-1) = -6 $ when evaluated at $ x = 2 $ and $ x = -1 $ respectively. All calculations have been shown step-by-step and justified for clarity.

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