Find the Quadratic Equation Passing Through Point (4,6)

To determine the correct equation, we need to consider the vertex form of a parabola:

• The vertex form is given by $y = a(x-h)^2 + k$ where $(h, k)$ is the vertex.
• In this problem, the vertex is $(4, 6)$.
• The equation becomes: $y = a(x-4)^2 + 6$.
• Since the parabola opens downwards, $a$ must be negative, implying $a = -1$.
• Thus, the equation is $y = -(x-4)^2 + 6$.

By comparing our derived expression with the options provided:

• $y=-(x-4)^2+6$ matches our derived equation.

Therefore, the correct equation is $y=-(x-4)^2+6$, corresponding to choice 3.