How do you graph #y= (x-4)^2 +3 #?

1 Answer
Meave60
Aug 24, 2015

Determine the vertex and several points, preferably on mirror images of the parabola. Plot points and sketch a curve through the points. Do not connect the dots.

Explanation:

#y=(x-4)^2+3#

The equation is in vertex form, #y=a(x-h)^2=k#, where #(h,k)# is the vertex, and #a=1#, #h=4#, and #k=3#. The vertex #(h,k)=(4,3)#.

Determine several points on the parabola, substituting both positive and negative numbers for #x#, and making sure to get points on both sides of the parabola. A mirror image is preferred. #y=(x-4)^2+3#

#x=0,# #y=19#
#x=1,# #y=12#
#x=2,# #y=7#
#x=6,# #y=7#
#x=7,# #y=12#
#x=8,# #y=19#

Plot the vertex and the points that you determined. Sketch a parabola (curve) through the points with the vertex as the minimum point. Do not connect the dots.

graph{y=(x-4)^2+3 [-15.09, 16.93, -1.09, 14.93]}

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