For this case, the function that has an axis of symmetry is given by:
\(f (x) = x ^ 2 - 6x - 1
\)
To verify this, what we must do is to derive the function, because the axis of symmetry passes through the minimum or maximum point of the function.
We have then:
\(f '(x) = 2x - 6
\)
From here, we equate the function to zero:
\(2x - 6 = 0
\)
Then, we clear the value of x.
We have then:
\(2x = 6
\)
\(x =\frac{6}{2}
x = 3
\)
Answer:
A function that has an axis of symmetry at x = 3 is:
\(f (x) = x ^ 2 - 6x - 1\)
