Diketahui fungsi g(x)=ax pangkat 2 + b. Jika g(2)=-1 dan g(-4)=5, nilai g(-1)+2=...

=== JAWAB ===

g(x) = ax² + b 
g(2) = a2² + b = -1
4a + b = -1

g(-4) = a(-4)² + b = 5
16 a + b = 5


4a + b = -1
16a + b = 5 
__________ - 
4a - 16a = -1 -5
-12 a = -6
a = [tex] \frac{1}{2} [/tex]

4([tex] \frac{1}{2} [/tex]) + b = -1
2 + b = -1
b = -3

g(x)= ax² + b
g(-1) = [tex] \frac{1}{2} [/tex] (-1)² - 3 = [tex] \frac{1}{2} [/tex] - 3 = [tex] \frac{1 - 6}{2} [/tex] = - [tex] \frac{5}{2} [/tex]

g(-1) + 2 = - [tex] \frac{5}{2} [/tex] + 2 = [tex] \frac{- 5+4}{2} [/tex] = - [tex] \frac{1}{2} [/tex]

[tex]g(x)=ax^{2}+b \\ \\ g(2)=-1 \\ a(2^{2})+b=-1 \to 4a + b = -1 \\ \\ g(-4)=5 \\ a((-4)^{2})+b=5 \to 16a+b=5 \\ \\ Eliminasi\ variabel\ "b" \\ 4a + b = -1 \\16a+b=5 \\ ------(-) \\ 4a-16a=-1-5 \\ -12a=-6 \\ \\ a= \frac{-6}{-12}= \frac{1}{2} \\ \\ Substitusikan\ nilai\ "a"\ ke\ persamaan\ 4a + b = -1 \\ 4.(\frac{1}{2}) + b = -1 \\ 2+b=-1 \\ b=-1-2 \\ b=-3 \\ \\ Fungsi\ g(x)\ adalah: \\ g(x)=\frac{1}{2}x^{2}-3[/tex]

Nilai g(-1) + 2 adalah :
[tex] g(x)=\frac{1}{2}x^{2}-3 \\ \\ g(-1) + 2=\frac{1}{2}(-1)^{2}-3 + 2 \\ \\ g(-1) + 2=\frac{1}{2}-1 \\ \\ g(-1) + 2=-\frac{1}{2}[/tex]