Solving a problem of quadratic function in Mathematics (11 points) It is known that the parabola y = x (square) + BX + C has only one intersection with the X axis, and the intersection is a (2,0) (1) Find the value of B.C (2) If the intersection of the parabola and the y-axis is B and the origin of the coordinate is O, find the perimeter of the triangle AOB (the answer can be with a root sign)

Solving a problem of quadratic function in Mathematics (11 points) It is known that the parabola y = x (square) + BX + C has only one intersection with the X axis, and the intersection is a (2,0) (1) Find the value of B.C (2) If the intersection of the parabola and the y-axis is B and the origin of the coordinate is O, find the perimeter of the triangle AOB (the answer can be with a root sign)

First of all, there is only one focal point with the x-axis, and the opening of the parabola is upward (because the prime coefficient is greater than 0), so it can only be the vertex, so the vertex is the point a. the symmetry axis X = 2. The formula of the symmetry axis is x = - B / 2a, that is x = - B / 2, because a = 1! So B = - 4. Then replace the coordinates of the point a into the formula, and you can calculate C = 4. I will calculate it orally, and you can calculate it again. Then you can find that the point B is (0,4), so the OA length is 2, The length of ob is 4. The length of AB is 2 square under the root sign + 4 square, and the perimeter can be calculated! Result 6 + 2 times the root sign 5

Trouble a math expert to help me solve a quadratic function problem
1. A machinery leasing company has 40 sets of machinery and equipment of the same type. After a period of operation, it is found that when the monthly rent of each set of machinery and equipment is 270 yuan, all of them are leased out. On this basis, when the monthly rent of each set of equipment is increased by 10 yuan, one less set of such equipment is leased out, Suppose the monthly rent of each set of equipment is x (yuan), and the monthly income (income = rental income expenses) of the leasing company is y (yuan)
(1) The algebraic expression containing x is used to express the number of equipment (sets) not leased and the expenses of all equipment (sets) not leased
(2) Find the quadratic function relation between Y and X;
(3) The monthly rent is 300 yuan and 350 yuan respectively. How much is the monthly income of the leasing company? How many sets of machinery and equipment should be rented at this time? Please give a brief explanation;
(4) Please formulate the quadratic function in (2) in the form of, and say that when x is what value, the leasing company's monthly income from leasing this type of equipment is the largest? What is the maximum monthly income?

(1) Let x = 300, x = 350 into the function of (2), and the solution is y = 1104011040. Because the income of the two is the same, they should be sold lower

A mathematical problem of quadratic function
A door opening is a parabola. The plane rectangular coordinate system is established by taking the straight line at the bottom of the door opening as the x-axis. The relationship of the parabola is y = - 2x square + 3. Then the width of the door opening at the two unit heights is,,, ha ha

This problem is not difficult, according to the equation you give, let y = 2, calculate the value of X. (take positive value, x = root 2 / 2)
Then the width is twice the value obtained, that is, the width is root 2

Given that f (x) is a quadratic function and f (x + 1) + F (x-1) = 2x & # 178; - 4x, find the value of F (1-radical 2)

Let f (x) = ax ^ 2 + BX + C
f(x+1)+f(x-1)=2a(x^2+1)+2bx+2c=2x^2-4x
Contrast coefficient: 2A = 2, 2b = - 4, 2A + 2C = 0
a=1,b=-2,c=-1
f(x)=x^2-2x-1
f(1-√2)=1+2-2√2-2+2√2-1=0