The function f(x) = -2(x-3)² + 7 has its vertex at (3, 7). What is f(5)?

Substitute $x=5$: $f(5)=-2(5-3)^2+7=-2(4)+7=-8+7=-1$, choice J. Choice F ($-15$) subtracts $7$ instead of adding it: $-8-7=-15$. Choice G ($7$) is the vertex's $y$-value, the maximum of the parabola, which occurs at $x=3$ and not at $x=5$. Choice H ($3$) is the vertex's $x$-coordinate. Since the parabola opens downward from a maximum of 7 at $x=3$, the value at $x=5$ must be less than 7, which rules out choice G immediately. Estimating before computing is a quick way to catch such a mistake.