Read+it!

//﻿Welcome to our final chapter!// As you saw in our last page Graph it!, we constructed an equation that gave us a curved line, unlike linear equations (ie: y = 2x+1), which give us straight lines.

That's right, faithful readers! Our investigation about gutters was only the beginning of a greater purpose! The areas that were calculated increased at the start, reached 8 sq. in. (our maximum area), and then decreased! We observed this behavior both in the chart we developed and the graph the calculator produced. This behavior is indicative of **quadratic equations**.


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

Furthermore, it's graph, the curve you saw in the former page, is called a **parabola.** To find the **maximum**, or **minimum**, value of a quadratic equation, there are two ways of finding them.
Firstly, we can find the highest point of the graph, seen below:



You can also find the maximum value using the equation. Quadratic equations in standard form look like this : ** y= ax 2 + bx + c .** From our equation, we gather the following:

The equation's minmum or maximum values can be found by using the following equation **x= -b/2a**. For our equation we calculate:
 * y = 8x - 2x 2 **** where a = -2, b = 8 and c = 0 **

**x= -(8) / 2(-2) = -8/(-4) = 2**

// **Therefore, the maximum value exists at x=2, and as we've already seen, y= 2(8-2(2)) = 2(8-4) = 2(4) = 8** //

// **﻿** // // **THANK YOU VERY MUCH FOR VISITING! If you enjoyed our presentation, feel free to stop by our history page, which explains the teaching method utilized here, Inductive and Deductive Teaching.** //

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