The image of quadratic function y = AX2 + BX + C (a > 0) has only one intersection point with X. A and Y axis intersect at point B, and OA = ob (1) The value of B (2) If the image of quadratic function y = AX2 + BX + C is translated 1 / a unit down and then h units to the left, let the parabola and X axis intersect at points c and D, which indicates the quantitative relationship between line CD and ob (3) Translate the image of quadratic function y = AX2 + BX + C down 1 / a unit, let the vertex of the parabola be e, and the parabola intersects the y-axis at point F. ask whether there is a point P on the parabola on the right side of the y-axis, so that the triangle PEF is isosceles triangle? If there is, find out the point P coordinate. If not, explain the reason

The image of quadratic function y = AX2 + BX + C (a > 0) has only one intersection point with X. A and Y axis intersect at point B, and OA = ob (1) The value of B (2) If the image of quadratic function y = AX2 + BX + C is translated 1 / a unit down and then h units to the left, let the parabola and X axis intersect at points c and D, which indicates the quantitative relationship between line CD and ob (3) Translate the image of quadratic function y = AX2 + BX + C down 1 / a unit, let the vertex of the parabola be e, and the parabola intersects the y-axis at point F. ask whether there is a point P on the parabola on the right side of the y-axis, so that the triangle PEF is isosceles triangle? If there is, find out the point P coordinate. If not, explain the reason

Take three points (1,0), (- 3,0), (0, - 3 / 2) into y = AX2 + BX + C to get
a+b+c=0
9a-3b+c=0
c=-3/2
Solution
a=1/2
b=1
c=-3/2
So the analytic formula is: y = 1 / 2x ^ 2 + x-3 / 2
Because 1 / 2 > 0, the opening of parabola is upward
Axis of symmetry x = - B / 2A = - 1 / 1 = - 1
Vertex coordinates (- B / 2a, (4ac-b ^ 2) / (4a)
-b/2a=-1
(4ac-b^2)/(4a)=-2
Vertex coordinates (- 1, - 2)

Ask 2 math questions, please answer quickly
1. There are two piles of coal. The original ratio of the first pile to the ground pile is 12:7. After a quarter of the coal is transported from the first pile, the second pile is 2.4 tons less than the first pile. How many tons of original coal is the first pile?
2. The number of boys in class 1 of grade 5 is one ninth more than that of girls. The ratio of girls to boys is (), and boys account for ()

1. Set up the first pile of original coal x tons
(1-1/4)x-7x/12=2.4 => x/6=2.4 => x=14.4
The first batch of original coal is 14.4 tons
2. The number of boys in class 1 of grade 5 is one ninth more than that of girls. The ratio of girls to boys is (9:10), and boys account for (10 / 19) of the class

1. There are 200 tons of coal in warehouse A and 80 tons in warehouse B. If 15 tons are transported out of warehouse a every day and 25 tons are transported in warehouse B every day, how many days will the two warehouses store the same amount of coal?
2. The school took the students to visit. It was estimated that it would cost 120 yuan / person for the people who planned to visit. Later, two people came in, and the total cost remained unchanged. So each person shared 3 yuan less. What was the number of students in this group?
3. The ratio of the amount that company a and company B are prepared to invest in a project is 6:7, company a invests 5 million yuan, company B invests 5 million yuan, and the ratio of the remaining amount of the two companies is 2:3?
4. The father is 41 years old and the son is 13 years old. After () years, the father's age is twice as old as the son's

1. Let the two warehouses be equal 200-15x = 80 + 25x25x + 15x = 200-8040x = 120x = 32 after X days, let the original group be x people 120x = (120-3) (x + 2) 120x = 117x + 234120x-117x = 2343x = 234x = 783, let a 6x yuan B 7x yuan (6x-500): (7x-500) = 2:314x-1000 = 18x-150018x-14x = 150