Question

medal and Fan!!!!!!!!!!
Using the completing-the-square method, find the vertex of the function f(x) = –2x2 + 12x + 5 and indicate whether it is a minimum or a maximum and at what point.

Answer 1

do you know what the vertex form equation looks like ?

Answer 2

You are given the parabola in the form

y = ax^2 + bx + c

need to turn into the form

y = a(x - h)^2 + k

by completing the square...

The vertex is the point (h,k) read directly from the equation.

Answer 3

\[f(x)=-2x^2+12x+5\\=-2(x^2-6x)+5\\=-2(x^2-6x+9-9)+5\\=-2(x-3)^2+18+5\\=-(x-3)^2+23\\vertex\ cab\ be\ found\ out\ by\ puttin'\ x-3=0\ \implies\ x=3(say\ \it\ h=3)\\for\ x=h=3, put\ f(x)=0\ get\ f(x)=23\ (say, \ k= 23)\\so\ vertex\ of \ function\ being\ a\ parabola\ is\ (h,k)=(3,23)\\ for\ minimum\ maximum\ use\ calculus\ \]