How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y=(x+5)^2-1#?

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Answer 1 · 2017-03-07T13:26:43

Please see below.

This is a typical quadratic equation in vertex form.

In a vertex form of equation such as #y=a(x-h)^2+k#

axis of symmetry is #x-h=0#

and maxima is at #x=h# and #y=k#, if #a<0# and minima is at #x=h# and #y=k#, if #a>0#

In #y=(x+5)^2-1#

axis of symmetry is #x+5=0#

and as #a=1#, we have a minima at #x=-5# and #y=-1# i.e. #(-5,-1)#

The graph appears as follows.
graph{(x+5)^2-1 [-9.625, 0.375, -2.66, 2.34]}