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 I've been trying to figure out why  $f\ left(x\ right)=\ SQRT{x+2}$ƒ (x)=x+2  IS a shift left 2.  I keep thinking that it IS +2 and that means right 2.

6 years ago

Answered By Jonny C

Recall in Math 20-1 that the standard form of a quadratic equation is y = a(x-p)^2+q were p is the horizontal translation and q is the vertical translation. In the context of this question it can be re-written as y = (x+2)^(1/2). But since the standard form of the equation is shown as NEGATIVE in y = a(x-p)^2+q, that means the value of p is actually -2 in your question, as two negatives make a positive. This might seem confusing but in reality the equation is y = (x-(-2))^(1/2). Since it's negative 2, it is a left shift.

For simplicity's sake, it's just easier to memorize this concept. Horizontal translation always move opposite of the sign (ie. negative is right shift, positive and left shift). Whereas vertical translation is always what you think it is (ie. positive is shift up, negative is shift down).

5 years ago

Answered By Sujalakshmy V

The function y=a Sqrt(x-c)) +d is the general transformation of the basic square root function y=Sqrt(x).

Where a represents the vertical strech about x axis.

 c represents horizontal translation and 

 d represents vertical translation.

 if c<0,the graph shifts to the left by c units

and if c>0, the graph shifts to the right by c units.

Here in our question, c is -2 since (x-(-2)) gives x+2. As c<0,the graph shifts to the left by 2 units.