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