Question

Convert Y=0.4(X -3)squared +4 to standard form

Answer 1

`Y=0.4X^2-2.4X+7.6`

Explanation:

Given:

The quadratic equation in vertex form is given as:

`Y=0.4(X-3)^2+4`

The standard form of a quadratic equation is:

`y=ax^2+bx+c`

Now, in order to convert the given equation into standard form, we have to expand
`(X-3)^2` using the binomial expansion given by:

`(a-b)^2=a^2+b^2-2ab`

Here,
`a=X\ and\ b= 3`

Therefore,

`(X-3)^2=X^2+3^2-2(X)(3)\\(X-3)^2=X^2+9-6X`

Now, plug in this expanded form into the original equation. This gives,

`Y=0.4(X^2+9-6X)+4`

Now, we use distribute 0.4 inside the parenthesis. This gives,

`Y=0.4X^2+(0.4*9)-(6X*0.4)+4\\Y=0.4X^2+3.6-2.4X+4\\Y=0.4X^2-2.4X+4+3.6\\Y=0.4X^2-2.4X+7.6`

Therefore, the standard form of the given equation is:

`Y=0.4X^2-2.4X+7.6`