# How do you sketch the graph of #y=(x+3)^2# and describe the transformation?

##### 1 Answer

May 28, 2017

#### Explanation:

#"the graph of " y=(x+3)^2" is the graph of " y=x^2#

#"translated 3 units to the left"#

#"the graph of " y=x^2" is "#

graph{x^2 [-10, 10, -5, 5]}

#" the point " (0,0)to(-3,0)#

#"choosing some values of x"#

#x=0toy=3^2=9to(0,9)larr" y-intercept"#

#x=-5toy=2^2=4to(-5,4)#

#"plot these points and draw a smooth curve through them"#

#"for the graph of " y=(x+3)^2#

graph{(x+3)^2 [-10, 10, -5, 5]}

#color(blue)"In general"#

#y=f(x+a)" is f(x) translated a units left "larr#

#y=f(x-a)" is f(x) translated a units right "rarr#