Question 1085926


1) 
Given the vertex form of this quadratic equation complete the following tasks:
{{{f(x)=(x+3)^2-2}}}
a) 
If {{{f(x)}}} is shifted three units to the right, shifted up two units, and reflected vertically over the x-axis, what is the new function?

Shifting to the right works the same way; {{{f (x - b)}}} is {{{f(x)}}} shifted {{{b }}}units to the {{{right}}}.

given {{{b=3}}}

{{{f(x)=(x+3-3)^2-2}}}

{{{f(x)=x^2-2}}}

to move a function {{{up}}}, you add outside the function: {{{f (x) + b}}} is {{{f (x)}}} moved up {{{b}}} units. 

{{{b=2}}}

{{{f(x)=x^2-2+2}}}

{{{f(x)=x^2}}}

and reflected vertically over the x-axis: {{{f(x)=-f(x)}}}

{{{f(x)=-x^2}}}-> your new function



{{{ graph( 600, 600, -10, 10, -10, 10, (x+3)^2-2, -x^2) }}}