Set 12: Quadratic Equations (Advanced)

Choice A is correct. Choice A is the correct answer. The x-coordinate of the vertex is given by $h = -b/2 a$. 1. Identify: $a=1, b=-8$. 2. Calculate h: $h = -(-8) / 2(1) = 8 / 2 = 4$. 3. Calculate k: Substitute $x=4$ back into the equation. $y = 4^2 - 8(4) + 12 = 16 - 32 + 12 = -4$. So the vertex is $(4, -4)$. Choice B is incorrect because it uses $x=-4$. Choice C is incorrect because of a sign error in calculation ($16 -32+12 \neq 4$). Choice D is incorrect because it uses $x=-4$.