## Unit Summary

In the standard form unit we learned how to change an equation from the various different forms into a standard form equation to find 3 points that can be used to plot a graph, also known as the 3 point method. We learned methods such as completing the squares, which is used to find the x's also known as the 0s of the parabola. we also learned how to find the maximum or minimum value of a quadratic relation

## Learning Goals

1)I am able to complete the squares to find the x's of a quadratic relation

3)I am able to graph a parabola using the 3 point method

## Word problem

A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft^2, what is the width of the path?

length times width = 400 sq/ft
(30-2x) * (20-2x) = 400

600 - 60x - 40x + 4x^2 = 400
4x^2 - 100x + 600 = 400
4x^2 - 100x + 600 - 400 = 0
4x^2 - 100x + 200 = 0; a quadratic equation

Simplify, divide by 4 and you have:
x^2 - 25x + 50 = 0

Completing the square is not a very good way to solve this

If you us the quadratic formula: a=1 b=-25 c=50

Two solutions:

x = 22.8, not a possible solution

x = 2.19 ft is the width of the path