Question

Standard to vertex form -x^2-3x+8

Answer 1

F(x) = - (x-(2/3))^2 41/2 = - (x 3/2) ^2

Answer 2

The vertex form:

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

(h, k) - vertex

`f(x)=ax^2+bx+c\\\\h=(-b)/(2a),\ k=f(h)`

We have

`f(x)=-x^2-3x+8\\\\a=-1,\ b=-3,\ c=8\\\\h=(-(-3))/(2(-1))=(3)/(-2)=-(3)/(2)\\\\k=f\left(-(3)/(2)\right)=-\left(-(3)/(2)\right)^2-3\left(-(3)/(2)\right)+8=-(9)/(4)+(9)/(2)+8\\\\=-(9)/(4)+(18)/(4)+(32)/(4)=(-9+18+32)/(4)=(41)/(4)\\\\Answer:f(x)=-\left(x-\left(-(2)/(3)\right)\right)^2+(41)/(4)=-\left(x+(3)/(2)\right)^2+(41)/(2)`