# Quadratics in Swimming

### Learn how quadratics can be applied in swimming.

## The Example of quadratics

Notice how the swimmer dives from the block into the water and once they enter the water and they pass the

__minimum value__and__vertex__,which is the lowest depth they reach in the water, to do the breakout stroke before coming back to the surface of the water (note that the__roots__are the points where the swimmer enters and comes back to the surface of the water).## Info

A swimmer dives from the block which is 1 foot above the deck (0,1) and once they enter the water, the lowest depth they achieve is 4 feet below the water (0,-4). The distance the swimmer swims till they resurface is 10 feet across (10,0) from the start.

## Work

With the information given the

__vertex__would be (5,-4) , the__axis of symmetry__would be x=5, the__minimum value__would be -4, the y-intercept would be (0,1).The equation in __standard form__ would be y=.18x^2+-1.9x+1. To convert into __Vertex form__ using the method of __completing the square__ would greatly help. () would go around the ax^2+bx making it (.18x^2+-1.9x)factor out the .18, then half the b value and using that new number subtract it from the original y value and square it then plug it in giving you the vertex form of

y= .18(x-5)^2+ 1

## Solutions

Plug in the equation to discover the solutions of {.6,10} meaning the swimmer will enter the water at ~.6 feet and resurface at ~10 feet from the starting position.

## Restraints

Domain={0<=x<=10}

Range={-4<=y<=1}