Question

Convert from vertex form to standard form. (3 pts). f(x) =(x-3)squared + 6

Answer 1

Standard form of
`f(x) =(x-3)^2 + 6` is
`\mathbf{x^2-6x+15}`

Explanation:

Convert from vertex form to standard form
`f(x) =(x-3)^2 + 6`

If the vertex form is:
`a(x-h)^2+k`

The Standard form is:
`ax^2+bx+c`

Now, converting
`f(x) =(x-3)^2 + 6` into standard form

We know that:
`(a-b)^2=a^2-2ab+b^2`

Using the formula:

`f(x) =(x-3)^2 + 6\\f(x)=x^2-2(x)(3)+9+6\\f(x)=x^2-6x+15`

So, Standard form of
`f(x) =(x-3)^2 + 6` is
`\mathbf{x^2-6x+15}`