As shown in the figure, the parabola y = a (x-1) &# 178; + 4 intersects the X axis at two points AB, and intersects the Y axis at point C. D is the vertex of the parabola, As shown in the figure, the parabola y = a (x-1) &# 178; + 4 intersects the X axis at two points AB, and intersects the Y axis at point C & nbsp; D is the vertex of the parabola, CD = √ 2, there are three points on the parabola, and the distance from the straight line BC is m, so find the value of M

As shown in the figure, the parabola y = a (x-1) &# 178; + 4 intersects the X axis at two points AB, and intersects the Y axis at point C. D is the vertex of the parabola, As shown in the figure, the parabola y = a (x-1) &# 178; + 4 intersects the X axis at two points AB, and intersects the Y axis at point C & nbsp; D is the vertex of the parabola, CD = √ 2, there are three points on the parabola, and the distance from the straight line BC is m, so find the value of M

A: parabola y = a (x-1) & # 178; + 4, opening downward a & lt; 0, point C (0, a + 4), point d (1,4) CD = √ (1 + A & # 178;) = √ 2, the solution is: a = - 1 (a = 1 does not conform to rounding), so: y = - (x-1) & # 178; + 4 and X-axis intersection a (- 1,0), B (3,0) point C (0,3), then BC line is y = - x + 3 to BC line