# determine coefficients of quadraticGiven (2,9) a point on the graph of f(x), what is t, if f(x) = x^2 - tx - 3?

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The function f(x) = x^2 - tx - 3. The point (2, 9) lies on the curve.

=> 9 = 2^2 - t*2 - 3

=> 9 = 4 - 2t - 3

=> 8 = 2t

=> t = 4

**The coefficient t = 4**

We'll replace x by 2 in the expression of f(x):

f(2) = 2^2-t*2-3

f(2) = 4 - 2t - 3

We'll combine like terms and we'll get:

f(2) = 1 - 2t

From enunciation, we know that (2,9) belongs to the graph of f(x) => f(2) = 9:

1 - 2t = 9

We'll isolate -2t to the left side.

-2t = 9 - 1 => -2t = 8

We'll divide by -2:

t = 8/-2

**The requested coefficient has the following negative value: t = -4**