Answer
True
Work Step by Step
RECALL:
The coordinates of the vertex of a quadratic function $f(x) = ax^2+bx+c$ are:
$\left(\frac{-b}{2a}, f(-\frac{2}{a})\right)$
The given quadratic function has $a=-1, b=4, c=5$.
Thus, the coordinates of the function's vertex are:
$=\left(-\frac{4}{2\cdot(-1)}, f(-\frac{4}{2\cdot(-1)})\right)
\\=\left(-\frac{4}{-2}, f(-(-2)\right)
\\=(2, f(2))$
The vertex has a y-coordinate of $f(2)$.
Therefore, the given statement is true.