Graph+it!

//Welcome to our next step: Interpretting our gutter area calculations! If you've wandered here before seeing the first part of the presentation, check it out here: Home//

Did you find a pattern in the areas you collected? Check your work against ours below:

//﻿// Did you find that the greatest Gutter Area is had when the side length is 2" and the bottom length is 4"? Great! What else did you noticed about these areas? To investigate further, let's construct an equation that will tie them all together!
 * ~ Side Length ||~ Bottom Length ||~ GutterArea ||
 * < 0.5" ||< 7" ||< 3.5 sq. in. ||
 * < 1" ||< 6" ||< 6 sq. in. ||
 * < 1.5" ||< 5" ||< 7.5 sq. in. ||
 * < 2" ||< 4" ||< 8 sq. in. ||
 * < 2.5" ||< 3" ||< 7.5 sq. in. ||
 * < 3" ||< 2" ||< 6 sq. in. ||
 * < 3.5" ||< 1" ||< 3.5 sq. in ||
 * < 4" ||< 0 ||< 0 ||

We started with the equation for finding areas, which is

**Area = Side Length x Bottom length**

At the beginning, the bottom length was 8" wide. After we folded our sides, the bottom length changed into the following

**Bottom length = 8" - 2(Side Length)**

If we substitute this expression into our equation for the area, we get

**Area = Side Length x (8" - 2(Side Length))**

If instead of the word 'area,' we use the letter 'y,' and instead of 'side length,' we use 'x' we get the following expression

**y = x (8- 2x)**

// Plug this equation in the graphing calculator to see what you get! After seeing what you can do with the calculator, head over to our final page, Read it! // //﻿// media type="custom" key="10649408"