We start with the equation y-k = a(x-h)^2. Since the vertex is at (1,1), this equation becomes y-1 = a(x-1)^2. Since the curve passes thru (0, -3), we get:
-3-1 = a(0-1)^2, or -4 = a. Thus, the eqn of the parabola is
y-1 = -4(x-1)^2. To find the x-intercepts, set y = 0 and solve the resulting equation for x:
-1 = -4(x-1)^2, or 1 = 4(x-2)^2, or (1/4) = (x-2)^2.
Taking the sqrt of both sides, (1/2) = plus or minus x-2.
Then x -2 = 1/2, or 2x - 4 = 1, or x = 5/2
Also, -(x-2) = 1/2, or -2(x-2) = 1, or -2x + 4 = 1, or -2x = -3, or x=3/2.
Thus, the x-intercepts are (3/2, 0) and (5/2, 0).
