What is the axis of symmetry and vertex for the graph #y=(1)(x-3)^2+(-1)#?

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Answer 1 · 2018-06-21T20:41:36

#"axis of symmetry" = 3#

#"vertex" = (3,-1)#

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

#y=(x-3)^2-1#

This quadratic equation is in vertex form:

#y=a(x+h)^2+k#

In this form:

#a = "direction parabola opens and stretch"#

#"vertex" = (-h,k)#

#"axis of symmetry" = -h#

#"vertex" = (3,-1)#

#"axis of symmetry" = 3#

finally, since #a=1#, it follows #a>0# then vertex is a minimum and the parabola opens up.

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