Question by NONAME: I am designing a logo for a company for my precalc class and i need help! “students design an appropriate logo
I am designing a logo for a company for my precalc class and i need help! “students design an appropriate logo for a company. They use a combination of conics (and other functions) to create their logo designs. Students must write equations, domains, and ranges that will reproduce the designs.” How do i start? I want to use a football as a logo, what is the domain and the range of the ellipse?
Is there a website that i can draw a picture and it tells me the domain range and the equations for everything?
Best answer:
Answer by ♫Ĵim βurne∬♪
The equation for an ellipse looks like:
(x – h)²/a² + (y – k)²/b² = 1
For example:
(x – 3)²/9 + (y – 7)²/25 = 1
Would be an ellipse with a center at (3, 7).
To draw it, first mark the center.
Then, count to the right √9 = 3 squares and mark the point (6, 7).
Then, starting at the center again, count to the left 0 squares and mark the point (0, 7).
Start again at the center but this time count up √25 = 5 squares, and mark the point (3, 12).
Then count down from the origin 5 squares and mark the point (3, 2).
Then draw the ellipse that connects those points.
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I’m not sure that “domain” and “range” properly apply to something that is not a function — which an ellipse is not, because it fails the “vertical line test” — but if the ellipse is written in standard form:
(x – h)²/a² + (y – k)²/b² = 1
Then the “domain” (in the sense of the x-values for which there will be at least one corresponding y-value) would be:
[h – a, h + a]
And the domain would be:
[k – b, k + b]
so for example:
(x – 3)²/9 + (y – 7)²/25 = 1
would have “domain” [3 – 3, 3 + 3] or [0, 6], and range [7 – 5, 7 + 5], or [2, 12].
Know better? Leave your own answer in the comments!