Question

Write the quadratic function in standard form.
f(x) = 6x^2 − x + 1

Answer 1

The equation in standard form is:

`f(x)=6(x-(1)/(12))^2-(23)/(24)`

Explanation:

Given function:

`f(x)=6x^2-x+1`

We need to convert this in standard form which is given by:

`f(x)=a(x-h)^2+k`

where
`a` represent co-efficient of leading term which is
`x^2`

and
`(h,k)` is the vertex (minimum and maximum point) of the curve.

`h` can be found out using formula
`h=(-b)/(2a)`

`a=6\ and\  b=-1`

`h=(-(-1))/(2(6))=(1)/(12)`

We can find
`k` by finding
`f(h)` as
`k=f(h)`.

`k=f((1)/(12))=6((1)/(12))^2-(1)/(12)+1`

`k=(6* (1)/(144))-(1)/(12)+1`

`k=(1)/(24)-(1)/(12)+1`

`k=(1-2+24)/(24)=(23)/(24)`

Thus the equation in standard form is:

`f(x)=6(x-(1)/(12))^2-(23)/(24)`