It is known that the parabola y = AX2 + BX + C intersects with X axis at two points a and B, and intersects with y axis at point C, where point B is on the positive half axis of X axis and point C is on the positive half axis of Y axis; the length of line OB and OC (OB < OC) is the two roots of equation x2-10x + 16 = 0, and the symmetry axis of parabola is a straight line x = - 2 (1) Find the expression of the parabola; (2) If point E is a moving point on line AB (not coincident with point a and point B), make ef ‖ AC through point E, intersect with point F and connect CE. When the area of △ CEF is the largest, calculate the coordinates of point E and the maximum area at this time; (3) If the moving line L parallel to the X axis intersects the parabola at point P and the line AC at point Q, the coordinates of point D are (- 3,0). Q: is there such a line L that △ odq is an isosceles triangle? If so, the coordinates of point P are requested; if not, please explain the reason

It is known that the parabola y = AX2 + BX + C intersects with X axis at two points a and B, and intersects with y axis at point C, where point B is on the positive half axis of X axis and point C is on the positive half axis of Y axis; the length of line OB and OC (OB < OC) is the two roots of equation x2-10x + 16 = 0, and the symmetry axis of parabola is a straight line x = - 2 (1) Find the expression of the parabola; (2) If point E is a moving point on line AB (not coincident with point a and point B), make ef ‖ AC through point E, intersect with point F and connect CE. When the area of △ CEF is the largest, calculate the coordinates of point E and the maximum area at this time; (3) If the moving line L parallel to the X axis intersects the parabola at point P and the line AC at point Q, the coordinates of point D are (- 3,0). Q: is there such a line L that △ odq is an isosceles triangle? If so, the coordinates of point P are requested; if not, please explain the reason

(1) By solving the equation x2-14x + 48 = 0, we can get X1 = 6, X2 = 8. From the meaning of the problem, we can get a (- 6,0), C (0,8), B (2,0) ∵ point C (0,8) on the image of parabola y = AX2 + BX + C, C = 8. Substituting a (- 6,0), B (2,0) into the expression, we can get {0 = 36a-6b + 80 = 4A + 2B + 8, we can get the solution {a = - 23B = - 83. ∵

It is known that the parabola y = AX2 + BX + C intersects the x-axis at two points AB, and intersects the y-axis at point C, where point a is on the negative half axis of x-axis and point C is on the negative half axis of y-axis

Question one
Solving x ^ 2-5x + 4 = 0, X1 = 1, X2 = 4 are the lengths of OA and OC, respectively|

The image of parabola y = AX2 BX C intersects with the negative half axis of X axis at a and the positive half axis of X axis at B and the Y axis at C (0, - 3) ob = OC (1) find the analytic expression of the quadratic function (2) let the vertex of the quadratic function be m and find am

This question lacks condition, a value cannot be determined
We can only know that the analytic formula of quadratic function is: y = a (x ^ 2) - 3, (a > 0)

When the vertex of a parabola is known to be at the origin, we can set the analytic expression of the parabola as
When the vertex of a known parabola is on the y-axis or the y-axis is the symmetry axis, but the vertex is not necessarily the origin, the parabola can be set as. When the vertex of a known parabola is on the x-axis, the analytical formula of the parabola can be set as, where (h, 0) is the intersection coordinate of the parabola and the x-axis

When the vertex of a parabola is known to be on the y-axis or the y-axis as the symmetry axis, but the vertex is not necessarily the origin,
Let the parabola be y = ax & # 178; + C;
When the vertex of the parabola is known to be on the x-axis, the analytic formula of the parabola can be set as y = a (X-H) &#;,
Where (h, 0) is the intersection coordinate of parabola and X axis