The quadratic function f is negative only on the open interval (−2, 1 4 ) and its graph passes through the point (−1, −5). Determine the coefficients of f and sketch its graph.

Answer 1

well, halfway between x axis intercepts is

x = 12/2 = 6 so that is where the vertex must be
y - b = (x-6)^2
-5 - b = (-7)^2 = 49
b = -54

y = (x-6)^2 - 54
y = x^2 - 12 x + 36 - 54
y = x^2 - 12 x - 18
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check:
x^2 - 12 x = y+18
x^2 - 12 x + 36 = y+ 54
(x-6)^2 = y + 54
(-1-6)^2 = -5 + 54
7^2 = 49 sure enough