# What are the vertex, axis of symmetry, maximum or minimum value, domain, and range of the function, and x and y intercepts for #f(x)=(x-5)^2 - 9#?

##### 1 Answer

Apr 29, 2015

This is an equation of a parabola, so we can find all the requests easily.

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- The vertex is
#V(5,-9)# . - The axis of symmetry is a vertical line passing from the vertex, so:
#x=5# . - The minimum is in the vertex (it is concave up!) and the maximum doesn't exist (it goes to
#+oo# ). - The domain is
#RR# , because it is a polynomial function. - The range is
#[5,+oo)# . - The x intercepts are points whose ordinate are
#0# , so:

#0=(x-5)^2-9rArr(x-5)^2=9rArrx-5=+-3rArr#

#x=5+-3rArrA(8,0)and B(2,0)# . - The y intercept is a point whose ascissa is
#0# , so:

#y=(0-5)^2-9rArr25-9=16rArrC(0,16)# .