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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. 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.

My fav brands: Chevy, the Ram trucks RAM symbol, and also the Dollar Tree logo

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.

In this case, a Christian Music business. Also, use only 8th grade graph functions

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 1

Part 1: Logo Research and Analysis

1. Chevy Logo (Bowtie Symbol):

   • The Chevy logo is a simple yet iconic bowtie shape. It uses straight lines and a bold presentation, which conveys strength and reliability. The metallic finish gives it a modern feel, appealing to car enthusiasts and everyday drivers alike. Its simplicity makes it easily recognizable, and it is often associated with American automotive culture.

2. Ram Trucks Logo:

   • The Ram symbol features a bold, stylized ram head with strong lines and curves. The design represents power and ruggedness, appealing to those looking for dependable trucks. The aggressive stance of the ram head conveys determination and strength, which resonates well with the target audience of truck users. It’s dynamic, and the choice of silver and black colors adds to its boldness.

3. Dollar Tree Logo:

   • The Dollar Tree logo is playful and inviting, featuring a bright green color that suggests freshness and value. The circular logo symbolizes community and accessibility, appealing to shoppers looking for great deals. The simple font combined with the cheerful graphic of a dollar sign reinforces the idea of affordability, making the brand immediately recognizable while emphasizing its core value of low prices.

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Part 2: Logo Design for a Christian Music Business

Design Overview: For the Christian Music business, I will create a logo that combines elements of faith and music. The logo will incorporate a cross as the central element, surrounded by musical notes, all within a circular shape.

Parent Function and Transformations:

1. Parent Function:

   • I will use the equation for a circle: \( (x - h)^2 + (y - k)^2 = r^2 \), where \( (h, k) \) is the center and \( r \) is the radius.

2. Transformations:

   • Translation: Move the circle to the center of the graph (e.g., shift it to (0, 0)).
   • Vertical Stretch: Modify the equation to stretch the height of the circle to emphasize the cross (e.g., change to \( (x - 0)^2 + 4(y - 0)^2 = 1 \)) to make it oval-shaped.

Logo Components:

• A cross (stylized) in the center of the logo.
• Musical notes extending outwards from the cross, adding a sense of movement and harmony.
• Color Palette:
  • Gold for the cross (symbolizing divinity and richness).
  • Deep blue for musical notes (representing peace and trust).
  • The background will be a soft white or light sky blue to ensure visibility.

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Part 3: Design Specifications and Pitch

Design Specifics:

• Equation for the oval from the transformation: \[ (x - 0)^2 + 4(y - 0)^2 = 1 \]
  • Domain: \( -1 \leq x \leq 1 \), \( -0.5 \leq y \leq 0.5 \).
• The cross can be represented with vertical and horizontal lines intersecting within the oval.
• Musical notes can be various shapes that emanate from the cross, featured around the oval.

Pitch: "This logo encapsulates the essence of our Christian Music business by combining the pillars of faith—represented by the cross—with the harmony of music, symbolized by the surrounding notes. The circular shape suggests a community united in worship, while the gold and blue colors invoke feelings of peace and devotion. It is designed to appeal to our audience of faith-driven individuals, inviting them to connect with their beliefs through music. This logo will not only attract attention but also resonate with the core values of our brand."