GIven Tx equals ax2 plus bx plus c find a b and c if T0 equals -4 T1 equals -2 and T2 equals 6?

Answer 1

T(x) = ax^2 + bx + c

T(0) = -4

T(1) = -2

T(2) = 6

Solution:

Since T(0) = -4, then c = -4.

So, when x = 1, we have:

-2 = a(1)^2 + b(1) - 4

-2 = a + b - 4

-2 + 4 = a + b - 4 + 4

2 = a + b

2 - a = a - a + b

2 - a = b

When x = 2, we have:

6 = a(2)^2 + b(2) - 4

6 = 4a + 2b - 4

6 + 4 = 4a + 2b - 4 + 4

10 = 4a + 2b

10/2 = 4a/2 + 2b/2

5 = 2a + b

5 - 2a = 2a - 2a + b

5 - 2a = b

2 - a = 5 - 2a

2 - 2 - a + 2a = 5 - 2 - 2a + 2a

a = 3

2 - a = b

2 - 3 = b

-1 = b

Thus, a = 3, b = -1, and c = -4.

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