How do you graph #y = (x+3)^2-1#?

1 Answer
Aug 26, 2015

Find the vertex and axis of symmetry. Plot the vertex. Determine points on both sides of the axis of symmetry. Plot the points. Sketch a curve to represent the parabola. Do not connect the points.

Explanation:

#y=(x+3)^2-1# is in the vertex form of a parabola, #y=a(x-h)-1#, where #h=-3 and k=-1#.

First find the vertex. The vertex of the parabola is the point #(h,k)=(-3,-1)#. This is the highest or lowest point on the parabola.

Next find the axis of symmetry. The is the line #x=h=-3#. This is the line that separates the two halves of the parabola into mirror images.

https://www.mathsisfun.com/algebra/quadratic-equation-graphing.html

Now determine some points on both sides of the axis of symmetry by substituting values for #x# in the equation. Plot the vertex and the points. Sketch a graph that is a curved parabola. Do not connect the dots.

#x=-5,# #y=3#
#x=-4,# #y=0#
#x=-2,# #y=0#
#x=-1,# #y=3#

graph{y=(x+3)^2-1 [-10, 10, -5, 5]}