Question

F(x)=x^2 +6x-8 Find range of f I found the range correctly as -17 but I don't know that where should be inequality sign direction?

Answer 1

`y inRR,y>=-17`

Explanation:

`"we require to find the vertex of the parabola and establish"`
`"if it is a maximum or minimum"`

`"the equation of a parabola in "color(blue)"vertex form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))`

`"where "(h,k)" are the coordinates of the vertex and a"`
`"is a multiplier"`

`"to obtain this form "color(blue)"complete the square"`

`rArry=x^2+2(3)x color(red)(+9)color(red)(-9)-8`

`rArry=(x+3)^2-17larrcolor(red)"in vertex form"`

`rArrcolor(magenta)"vertex "=(-3,-17)`

`"since "a>0" then minimum "uuu`

`"range is "y inRR,y>=-17`

`y in[-17,oo)larrcolor(blue)"in interval notation"`
graph{x^2+6x-8 [-40, 40, -20, 20]}