# If f(x)= 6x^2+ ax + c, f(2)= 8 and f(5)= 12 what is a and c?

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f(x) = 6x^2 + ax + C

Given f(2) = 8 and f(5) = 12

==>f(2) = 6(2^2) + a(2) + C = 8

==> 24 + 2a + C = 8

==> 2a + C = -16.........(1)

f(5) = 6(5^2) + a(5) + C = 12

==> 150 + 5a + C = 12

==> 5a + C = -138...........(2)

Using the elimination method, we will subtract (1) from (2):

==> 3a = -122

**==> a = -122/3 **

==> C = -16 - 2a

= -16 - 2(-122/3)

= -16 + 244/3

= 196/3

**==> C = 196/3 **

f(2)=8 6*2^2+2a+c=8 24 +2a+c=8 2a+c=-16(1)

f(5)=12 6*5^2+5a+c=12 150+5a+c=12 5a+c=-138(2)

we have(1) 2a+c=-16 0r -2a-c=16

5a+c=-138(2)

3a =-122

a=-122/3

c=-16-2a=-16-2*(-122/3)=-196/3