Question 1196172
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Plug in x = -2
g(x) = a*x^2 + b*x + 2
g(-2) = a(-2)^2 + b(-2) + 2
g(-2) = a(4) + b(-2) + 2
g(-2) = 4a - 2b + 2
6 = 4a - 2b + 2
6-2 = 4a - 2b
4 = 4a - 2b


Let's solve for b
4 = 4a - 2b
4+2b = 4a
2b = 4a-4
b = 4a/2-4/2
b = 2a - 2


Now plug in x = 3
g(x) = ax^2 + bx + 2
g(3) = a(3)^2 + b(3) + 2
11 = 9a + 3b + 2


From here, plug in b = 2a - 2 and solve for 'a'
11 = 9a + 3b + 2
11 = 9a + 3(2a-2) + 2
11 = 9a + 6a-6 + 2
11 = 15a-4
15a-4 = 11
15a = 11+4
15a = 15
a = 15/15
a = 1


Then,
b = 2a-2
b = 2(1)-2
b = 2-2
b = 0



Answers:
a = 1
b = 0
The function is g(x) = x^2+2
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