Find the vertex of the quadratic function given below.
f(t) = (x – 4)(x + 2)
A.
B.
(1,-9)
(-4,2)
C. (-1,9)
OD. (4,-2)
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One way to do it is to expand the quadratic, then complete the square to write it in vertex form:

Then we get the vertex right away, (1, -9).

Alternatively, if you know about the parity/symmetry of parabolas, you know that the vertex lies on a line between its roots. In this case, we know and are the roots to this quadratic. The line falls in the middle of these two points (if you're unsure as to why, take the average of the roots: (4 - 2)/2 = 1). So we know the -coordinate of the vertex, and the -coordinate is , so we again get (1, -9).

The answer is (1, -9) which is the vertex otherwise known as the minimum. It is where the graph comes to a curve.

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