Question
Imagine you are working in the advertising department for a new brand. During your first meeting, the executives state that they need a logo that will catch people’s attention. In order to solve this problem, it is your job to research logos and create one that will fit the company’s brand. Part 1 Research current and past logos used by a variety of companies. Think about your favorite brands. What type of shapes or lines do they use in their logos? Choose two or three logos and describe why each one is appealing to you. Part 2 Use computer technology or a piece of paper to design your own logo. Use at least one parent function and two transformations in your logo design. Part 3 Write up the specifics of your design so that the advertising department’s art team can create a finalized version. You should include the equations you used in your design, along with any domain restrictions or important intersection points. You should also include relevant information about colors. Finally, write a short pitch (3–5 sentences) about why your logo is the best choice for your company and why you think it will appeal to buyers.
Answer each question in 2-3 sentences
Answer each question in 2-3 sentences
Answers
GPT-4o mini
### Part 1
I researched logos from various brands, including Nike and Apple. The Nike logo, known as the "Swoosh," is appealing due to its simplicity and dynamic shape, which conveys motion and energy. Apple’s logo, a stylized apple with a bite taken out, is memorable and sophisticated, using clean lines and a modern aesthetic to represent innovation and quality. Both logos effectively utilize negative space and minimalism, making them easily recognizable and versatile across various media.
### Part 2
For my logo design, I chose to create a stylized letter "X" using the parent function of a quadratic equation: \( f(x) = x^2 \). I applied a vertical stretch and a horizontal compression. The transformations produced an elongated "X" that is symmetrical and visually striking. Additionally, I incorporated circular arcs at the tips of the "X" to represent inclusivity and connection.
### Part 3
The specifics of my design include the equations:
1. For the quadratic curve of the "X": \( f(x) = 2x^2 \) (vertical stretch).
2. For the horizontal compression: \( g(x) = (2x)^2 = 4x^2 \).
The domain restriction is \( x \in [-2, 2] \), which allows the logo to maintain its intended shape. The colors chosen are a deep navy blue for the main elements, symbolizing trust and reliability, paired with a vibrant orange for the arcs, representing creativity and energy.
My pitch for this logo is that it encapsulates both modernity and stability, appealing to customers who value innovation and quality. The striking color contrast and unique shape ensure it stands out in a crowded market, making it memorable and relatable, ideal for attracting a diverse customer base.
I researched logos from various brands, including Nike and Apple. The Nike logo, known as the "Swoosh," is appealing due to its simplicity and dynamic shape, which conveys motion and energy. Apple’s logo, a stylized apple with a bite taken out, is memorable and sophisticated, using clean lines and a modern aesthetic to represent innovation and quality. Both logos effectively utilize negative space and minimalism, making them easily recognizable and versatile across various media.
### Part 2
For my logo design, I chose to create a stylized letter "X" using the parent function of a quadratic equation: \( f(x) = x^2 \). I applied a vertical stretch and a horizontal compression. The transformations produced an elongated "X" that is symmetrical and visually striking. Additionally, I incorporated circular arcs at the tips of the "X" to represent inclusivity and connection.
### Part 3
The specifics of my design include the equations:
1. For the quadratic curve of the "X": \( f(x) = 2x^2 \) (vertical stretch).
2. For the horizontal compression: \( g(x) = (2x)^2 = 4x^2 \).
The domain restriction is \( x \in [-2, 2] \), which allows the logo to maintain its intended shape. The colors chosen are a deep navy blue for the main elements, symbolizing trust and reliability, paired with a vibrant orange for the arcs, representing creativity and energy.
My pitch for this logo is that it encapsulates both modernity and stability, appealing to customers who value innovation and quality. The striking color contrast and unique shape ensure it stands out in a crowded market, making it memorable and relatable, ideal for attracting a diverse customer base.