How do you use the important points to sketch the graph of #f(x)=3-x^2-2x#?

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Answer 1 · 2016-09-17T11:12:32

#f(x)# has zeros at #x=-3 and 1#
#f(x) # has a maximum at #(-1,4)#

#f(x) = 3-x^2-2x#
#f(x) = 0 -> x^2+2x-3=0#
#-> (x+3)(x-1)=0#

Hence #f(x)# has zeros at #x=-3 and 1#

#f'(x) = -2x-2#
#f(x)# has a turning point where #f'(x)=0#

#f'(x) =0 -> -2x-2=0 -> x=-1#

Since the coefficient of #x^2# is negative #f(-1)# is a maximum value of #4#

These points can be seen on the graph of f(x) below.

graph{3-x^2-2x [-11.25, 11.25, -5.62, 5.63]}