xy12345–1–2–3–4–5–612345–1–2–3–4–5–6ABCo已知抛物线,与x轴交于A(-3,0)、B(1,0),与y轴交于点C,(1)求抛物线的解析式及顶点坐标;(2)在平面直角坐标系中,是否存在点D,是以A、B、C、D为顶点的四边形为平行四边形,若存在,请直接写出点D的坐标,若不存在,请说明理由.(3)在抛物线的对称轴上是否存在点M,使△BCM为直角三角形,若存在,请求出点M的坐标,若不存在,请说明理由.xy(-2,-3)(-4,3)(4,3)D3D1D212345–1–2–3–4–512345–1–2–3–4–5ABCo,(-1,4)xyHGM12345–1–2–3–4–5–612345–1–2–3–4–5–6ABCo,xyHGM12345–1–2–3–4–5–612345–1–2–3–4–5–6ABCoxyHM12345–1–2–3–4–5–612345–1–2–3–4–5–6ABCoxy12345–1–2–3–4–5–612345–1–2–3–4–5–6ABCo(4)在抛物线的对称轴上是否存在点P,使△BCP为等腰三角形,若存在,请求出点P的坐标,若不存在,请说明理由.xyP1P212345–1–2–3–412345–1–2–3–4–5ABCoxyP312345–1–2–3–4–5–612345–1–2–3CBAoxyP5舍去P412345–1–2–3–4–5–612345–1–2–3–4–5CBAoxy12345–1–2–3–4–5–612345–1–2–3–4–5–6ABCo(5)在抛物线的对称轴上是否存在点Q,使△ACQ为直角三角形,若存在,请求出点Q的坐标,若不存在,请说明理由.xyQ112345–1–2–3–4–512345–1–2–3–4–5ABCoxyIQ212345–1–2–3–4–512345–1–2–3–4–5ABCoxyO1Q3Q412345–1–2–3–4–512345–1–2–3–4–5ABCo,xyFE12345–1–2–3–412345–1–2–3–4–5–6ABCo(6)若点E从点C出发,沿线段CB向点B运动,F从点B出发,沿线段BA向点A运动,两点同时出发,速度分别为每秒个单位长度和每秒3个单位长度,点F运动到A即停止,设运动时间为t秒.①设△BEF的面积为S,求S与t之间的函数关系式,并求t为何值时,△BEF的面积最大,最大值是多少?②当△BEF为等腰三角形时,求运动时间t的值.BF=BE,,EF=EB,,FE=FB,