Latihan dan Pembahasan

1.       Suatu fungsi kuadrat mempunyai nilai minimum -2 untuk x=3 dan

untuk x=0 nilai fungsi itu 16. Fungsi kuadrat itu adalah….

a.       f(x) = x² +6x +8                          d. f(x) = 2x² – 12x +16

b.      f(x) = x² -6x + 8                          e. f(x) = 2x² – 12x -16

c.       f(x)=2x² +12x +16

Pembahasan:

fungsi kuadrat dengan nilai minimum -2 untuk x = 3

adalah f(x)=a(x-3)² -2

f(0)=16             f(0)=a(0-3)² -2 =16

9a=18

A                             =2

\      fungsi kuadrat f(x)=2(x-3)² -2

           f(x)=2x²-12x+16

          2. nilai maximum dari fungsi f(x)=-2x² +(k+5)x+1-2k adalah 5

                Nilai k yg positive adalah…

                a. 1                         c.7                          e.9

                b.5                          d.8

  Pembahasan :

Nilai maximum adalah y= = -

f(x) = -2x² +  (k=5)x + 1 -2k

Nilai maksimum : y = - - = 5

-      

-      

                                      K²-6k+33=40

                                        K²-6k-7=0

                                       (k+1) (k-7)=0

                                      K=-1 atau k=7

 

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