Question

Can I get some help please? Thanks!

For the given quadratic equation convert into vertex form, find the vertex, and find the value for x = 6. Show your work.
`y = -2x^2 + 2x +2`

Answer 1

See explanation.

Explanation:

To find the value of `f(x)` for `x=6` you have to substitute `6` for every occurence of `x` in the formula:

`f(color(red)(6))=-2*color(red)(6)^2+2*color(red)(6)+2=-2*36+12+2=`

`=-72+14=-58`

To convert to the vertex form you can use:

The vertex form of a quadratic function is:

`f(x)=a(x-p)^2+q`

where:

`p=-b/(2a)`

and

`q=(-Delta)/(4a)`

Here we have:

`a=-2`; `b=2`; `c=2`, so:

`p=(-2)/(2*(-2))=(-2)/(-4)=1/2`

`Delta=b^2-4ac=4-4*(-2)*2=4+16=20`

`q=(-20)/(4*(-2))=(-20)/(-8)=2 1/2`

Finally we can write the vertex form:

`f(x)=-2*(x-1/2)^2+2 1/2`