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
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