∴{? 4? 2b+c=0，？ 16+4b+c=0, the solution is: {b=2, c=8,
∴y=？ x2+2x+8。
2. For OH∑AC passing through point O and at point H,
∵A(？ 2，0)、B(4，0)，
∴OA=2,OB=4,AB=6，
∫D is the midpoint of OC,
∴CD=OD，
∵OH∨AC，
∴OHCE=ODCD= 1，
∴OH=CE，
∴CEAE=OHAE=BOBA，
∴CEAE=23.
3. point c is CF⊥AB, and the vertical foot is point f,
Let C(x,? X2+2x+8), and then F(x, 0),
∴AF=x+2,CF=？ x2+2x+8，
∫ in Rt△AFC, tan∠CAB=CFAF=2,
∴? x2+2x+8x+2=2，
Solution: x=2,
∴C(2,8)，
∴S△AOC= 12×2×8=8，
Connect OE so that s △ CDE = y.
OD = CD，
∴S△ODE=S△CDE=y，
∴S△OCE=2y，
∫CEAE = 23，
∴S△OCES△AOE=23，
∴S△OAE=3y，
∴S△OAC=5y，
∴5y=8，
∴y=85.
The area of CDE is 85.
Extended data:
Parabolic junior high school knowledge arrangement
1, parabola is an axisymmetric figure. The symmetry axis is a straight line x = -b/2a.
The only intersection of the symmetry axis and the parabola is the vertex p of the parabola. Especially when b=0, the symmetry axis of the parabola is the Y axis (that is, the straight line x=0).
2. The parabola has a vertex p, whose coordinates are: P (-b/2a, (4ac-b 2)/4a) When -b/2a=0, p is on the Y axis; When δ = b 2-4ac = 0, p is on the x axis.
3. Quadratic coefficient A determines the opening direction and size of parabola.
When a>0, the parabola opens upwards; When a<0, the parabola opens downward. The larger the |a|, the smaller the opening of the parabola.
4. Both the linear coefficient b and the quadratic coefficient a*** determine the position of the symmetry axis.
When A and B have the same number (ab>0), the symmetry axis is on the left side of Y axis;
When a and b have different numbers (i.e. AB
5. The constant term c determines the intersection of parabola and Y axis.
The parabola intersects the Y axis at (0, c)
6. Number of intersections between parabola and X axis
δ= b^2-4ac>； 0, parabola and x axis have two intersections.
When δ = b 2-4ac = 0, there are 1 intersections between parabola and X axis.
δ= b^2-4ac<； 0, the parabola has no intersection with the x axis. The value of x is an imaginary number (the reciprocal of the value of x =-b √ b 2-4ac, multiplied by the imaginary number I, and the whole formula is divided by 2a).