How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y=(x+1)^2 - 4#?

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Answer 1 · 2018-05-08T06:41:24

Axis of symmetry: #x=-1 forall y#
Graph parabola
#y_min = -4#

#y=(x+1)^2-4#

#= x^2+2x-3#

#y# is a quadratic function of the form #ax^2+bx+c# which will have a parabolic graph.

The axis of symmetry will occur where #x=-b/(2a)#

#:. x= -2/(2xx1) =-1#

Hence, the axis of symmetry is the vertical line #x=-1 forall y#

Since #a>0, y# will have a minimum value on the axis of symmetry.

Thus, #y_min = (-1)^2+2(-1)-3#

# = 1-2-3 = -4#

The graph of #y# is shown below.

graph{(x+1)^2-4 [-6.406, 6.08, -4.64, 1.6]}