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

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estanbuen | Student | (Level 1) eNoter

Posted September 21, 2010 at 7:32 AM via web

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

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted September 21, 2010 at 7:38 AM (Answer #1)

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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

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phucnguyen08 | Student, College Freshman | (Level 1) Honors

Posted September 28, 2010 at 1:47 PM (Answer #2)

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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

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