How do you describe the end behavior for #f(x)=-x^2-8x-15#?

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Answer 1 · 2018-01-13T15:18:44

See below.

For end behaviour of a polynomial, we only have to look at the leading coefficient and degree. In this case:

#-x^2#

as #x->-oo# , #color(white)(888)-x^2->-oo#

as #x->oo# , #color(white)(888)-x^2->-oo#

#x^2>0color(white)(888)# for all #RRcolor(white)(888)#, so #color(white)(8)-x^2<0# for all #RR#

Since the coefficient of #x^2<0#, the parabola is of the form:

#nnn#

GRAPH:

graph{y=-x^2-8x-15 [-10, 5, -5, 4]}