OG详解-OG8 数学1 Q25

Choice C is correct. In the xy-plane, the graph of the line y= c is a horizontal line that crosses the y-axis at y= c and the graph of the quadratic equation y=-x² +9x-100 is a parabola. A parabola can intersect a horizontal line at exactly one point only at its vertex. Therefore, the value of c should be equal to  the y-coordinate of the vertex of the graph of the given equation. For a quadratic equation in vertex form, y= a(x-h)² +k, the vertex of its graph in the xy-plane is  (h, k). The given quadratic equation, y=-x² +9x-100, can be rewritten as y=-（x² -2(92​​)x +(92​​) ² ）+ (92​)^2​ -100, or y= - ( x−​92​ ) ²+ (- 319​4​) the value of c is equal to −​3194​.
Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.