Answer
$\bf{True}$.
Work Step by Step
The coordinates of the vertex of a quadratic function $f(x) = ax^2+bx+c$ are given by: $\displaystyle(\frac{-b}{2a}, f(-\frac{2}{a}))$
We see that the given quadratic function has the coefficients:
$a=-1, b=4, c=5$.
Therefore, the coordinates of the function's vertex can be expressed as:
$(-\dfrac{4}{2\cdot(-1)}, f(-\dfrac{4}{2\cdot(-1)}))=(-\dfrac{4}{-2}, f(-(-2))
\\=[2, f(2)]$
So, the vertex has a y-coordinate of $f(2)$.
Therefore, the given statement is $\bf{True}$.
