For this case we have the following function:
\(f (x) = (x-6) (x + 2)
\)
We rewrite the function making distributive property.
We have then:
\(f (x) = x ^ 2 + 2x - 6x - 12
f (x) = x ^ 2 - 4x - 12
\)
To find the vertex of the function, we derive:
\(f '(x) = 2x - 4
\)
We equal zero and clear the value of x:
\(2x - 4 = 0
2x = 4
\)
\(x = \frac{4}{2}
x = 2
\)
We evaluate the function for the value of x obtained:
\(f (2) = (2) ^ 2 - 4 (2) - 12
f (2) = 4 - 8 - 12
f (2) = -16
\)
Then, the vertice of the parabola is:
\((x, y) = (2, -16)
\)
Answer:
the vertex of the quadratic function f(x)=(x-6)(x+2) is:
\((x, y) = (2, -16)\)
