OG详解-OG1 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 they-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  they-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 asThus, the value of c  is equal to - 3194​​