中四數學問題 (Quadratic Function)

Since the coordinates of the vertex of the graph are (3,15),
y = f(x)= a(x-3)^2+15

The statement of "the graph touches at one point (0,-2) at x-axis" is wrong. At (0,2), the point is on y-axis since the x-coordinate is 0. But the y-coordinate is non-zero. Therefore the point is not on x-axis.

If the correct statement is "the graph touches at one point (0,-2) at y-axis",
When x=-2, y=0
0 = a(-2-3)^2+15
a = -3/5

Therefore the model answer of f(x) = -3/5*(x-3)^2+15 = -3/5*(x+2)(x-8) is obtained.

2013-06-08 12:17:12 補充：
The correct statement is "the graph touches at one point (-2,0) at x-axis"

The question should reads "the graph cuts the x-axis at (-2,0)"