Parabola y = 1 / 2x & # 178; + 1 can be regarded as parabola y = 1 / 2 (x + 3) &# 178; along X axis_ Translation_ Unit

Parabola y = 1 / 2x & # 178; + 1 can be regarded as parabola y = 1 / 2 (x + 3) &# 178; along X axis_ Translation_ Unit

The X axis moves three units to the right and one unit up

The parabola y = - 3 (x-1) ^ is translated upward by K units, and the intersection of the parabola and the X axis is at points a (x1,0) and B (x2,0). If (x1) ^ + (x2) ^ = 26 / 9, then K=

y=-3(x-1)^2+k
3x^2-6x+3-k=0
x1+x2=2 x1x2=(3-k)/3
x1^2+x2^2=(x1+x2)^2-4x1x2=4-4(3-k)/3=26/9
k=25/6

If the parabola y = a (X-H) ^ 2 is translated 3 units to the left to get the parabola y = - 2 (x-1) ^ 2, then a=__ ,h=__ .

Solution
Y = a (X-H) &# 178; 3 units to the left
y=a(x+3-h)²
=-2(x-1)²
∴
a=-2,3-h=-1
∴a=-2,h=4

The parabola y = ax & sup2; + BX + 3 intersects the y-axis at point C, and intersects the x-axis at two points a and B, Tan ∠ OCA = & # 8531;, s Δ ABC = 6
Let point e be on the x-axis and point F be on the parabola. If a, C, e and f form a parallelogram, please write out the coordinates of point E

The coordinates of point e are (7,0)
A (1,0), B (5,0)
So the parabola is y = 0.6x ^ 2-3.6x + 3
Then the abscissa of F is 6, CF = 6
Move a 6 units to the right to get e (7,0)