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#

1 Answer
Daniel L.
Sep 13, 2017

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#

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