Question

May you simply explain this concept I've been lost on this all day.

Answer 1

`(x+(5)/(2))^2-(1)/(4)`

Step-by-step explanation:

Given a quadratic equation of the form:

`y=ax^2+bx+c`

To "complete the squares" is to rewrite it as:

`y=a(x+d)^2+e`

Where:

`d=(b)/(2a)`
`e=c-(b^2)/(4a)`

In this case, we are given:

`y=x^2+5x+6`

Then:

a = 1

b = 5

c = 6

Using the formulas above:

`d=(5)/(2\cdot1)=(5)/(2)`
`e=6-(5^2)/(4\cdot1)=6-(25)/(4)=-(1)/(4)`

Now, we can rewrite:

`y=(x+(5)/(2))^2-(1)/(4)`