How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y= 3(x+2)^2-1#?

1 Answer
Jul 17, 2018

Minimum #(-2, -1); " axis of symmetry: " x = -2#

Explanation:

Given: #y = 3(x+2)^2 - 1#

The given function is a quadratic equation that is the graph of a parabola.

When the equation is in vertex form: #y = a(x - h)^2 + k#,

the #"vertex": (h, k); " axis of symmetry: "x = h#

The parabola has a minimum when #a >0# and a maximum when #a < 0#

the #"vertex": (-2, -1); " axis of symmetry: "x = -2#

the vertex is a minimum since #a = 3 > 0#

To graph just find additional points using point-plotting. Since #x# is the independent variable, you can select any value of #x# and calculate the corresponding value of #y#:

#ul(" "x" "|" "y" ")#
#-4" "|" "11" "#
#-3" "|" "2" "#
#-1" "|" "2" "#
#" "0" "|" "11" "# This is the #y#-intercept

Graph of #3(x+2)^2 - 1#:
graph{3(x+2)^2 - 1 [-5, 3, -5, 12]}