6.2 SUPPORTING PATH quadratic formulas

Theory

Quadratic formulas are formulas who have a squared letter (a number multiplied by itself). Those formulas are used to calculate things in a fast and easy way.

Those are examples of how quadratic formulas look like:

y = 5x²+ 2
y = a²
b=3c²

You also need to know how to calculate with those kind of formulas.

Example

A princess is living in a big castle with a big garden in the shape of a square.

This is how her garden looks like:

Quadratic formulas, garden, roses, math, squares, quadratic formulas.

The garden consists of squared bricks which are grey and the garden is enclosed with red roses.

One day, the princess decides to have a bigger garden and she calls her gardener. She asks him to make her garden two times as wide and two times as long. After he has finished he has to put the red roses back around her garden.

Before he is going to start she wants to know how many bricks + roses they need to have in total, this total is called the total amount.

The gardener is making a calculation for the princess:

He is giving the grey bricks the letter x.

The total amount of bricks+roses are called y.

There are 8 red roses, the 8 roses just stay the same, the gardener is going to enlarge the garden and afterwards he is going to put the 8 roses back, so the roses won't increase.

8

x

y

So, the formula that the gardener is going to use is: Total amount = Grey bricks ^. Grey bricks + 8 roses.

With the correct letters the formula will be:

y = x²+ 8

(Because x ^. x = x²)

The gardener now has an easy way to calculate the total amount of brick and roses if the princes wants to enlarge her garden again.

The length of the garden consists of 5 blocks, if the princess is going to double it , it will consist out of 10 bricks. So, we have to fill in 10 for x.

y = 10²+ 8

y = 100 + 8 = 108

So, the total amount of bricks and roses which the princess and the gardener will need is 108.