How do you sketch the graph of #y=x^2-5# and describe the transformation?

Question

Nathan Axel · Accepted Answer

See graph and explaination

#y=x^2 #graph{x^2 [-10, 10, -5, 5]} Let's first look at the graph #y=x^2# If you have a graphing calculator then plot this and then go to the table of values. #y=x^2-5# graph{x^2-5 [-10, 10, -5, 5]} Now lets look at #y=x^2-5#. To describe the transformation going on we can see that the function can been shifted down (or translated) down #5# units but how exactly do we know this? Well, graphically speaking we can see this going on if we take the point #(0,0)# from #y=x^2# and see where it's located in the function #y^2-5#. We find that its now at #(0,-5)# so we say that the graph has been translated down #5# units. Algebraically, if the above is true for the point #(0,0)# then it must be true for all points on the graph #y-x^2#. Thus, we translate (or shift) down #5# units for every point on the graph #y=x^2# (Note: We are changing the #y# value for each point so #(0,0)# on #y=x^2# is now #(0,-5)# on #y=x^2-5# NOT #(-5,-5). I hope this explanation proved to be very helpful and good luck! ;)

Kennedy Adams · Answer

undefined To sketch the graph of y = x^2 - 5, start with the basic quadratic function y = x^2 and shift it downward by 5 units. This transformation moves the entire graph down. The vertex of the parabola will be at (0, -5), and the shape of the graph remains the same as the basic quadratic function.