Mathematical quadratic function It is known that the parabola y = ax ^ 2 + BX + C intersects the x-axis at two points a and B (point B is on the right side of point a, and ab = 8), and intersects the y-axis at point C, where point a is on the negative half axis of x-axis, point C is on the positive half axis of y-axis, and the length (OA) of line segments OA and OC

Mathematical quadratic function It is known that the parabola y = ax ^ 2 + BX + C intersects the x-axis at two points a and B (point B is on the right side of point a, and ab = 8), and intersects the y-axis at point C, where point a is on the negative half axis of x-axis, point C is on the positive half axis of y-axis, and the length (OA) of line segments OA and OC

By the length (OA) of line OA, OC

Quadratic function
If the vertex of the parabola y = - 9 (x + 3) ² + 1-k is on the X axis, then K=
The parabola y = a (x + 3) &# 178; (a ≠ 0) must have an intersection with the coordinate axis

(1) If the abscissa of the vertex is - 3, the ordinate is 1-k, and the vertex is on the X axis, then y = 1-k = 0, and the solution is k = 1
(2) From the vertex formula, we can see that the vertex is (- 3,0). If it is on the x-axis, other points cannot be on the x-axis (according to the parabola image), so there must be one intersection point
Or let y = a (x + 3) ^ 2 = 0, eliminate a, square root, get x + 3 = 0, have unique solution, so there must be 1 intersection

The analytic expression of quadratic function
Given the parabola y = x ^ 2 + (A-2) x-2a (a is a constant, a > 0), let the two intersections of the parabola and the X axis be A.B (a is on the left side of B), and the intersection of the parabola and the Y axis be c. when AC = 2 pieces of 5, the analytical formula of the parabola is obtained

y=(x+a)(x-2)
A (- a.0) B (2.0) Note: here y = 0
Note: here x = 0
AC ^ 2 = (- a) ^ 2 + (- 2A) ^ 2. It can be calculated by Pythagorean theorem or vector length here. Of course, the former is easier to think of
The root of AC = a times 5
So a = plus or minus 2
A = - 2 is not satisfied with the problem stem (only one focus)
So a = 2
The result is y = x ^ 2-4

What does it mean that the derivative of a function is continuous

For example, the absolute value of ~ y = x is continuous, but the derivative is discontinuous
For example, y = x square, when x is greater than 0, y = x square, when x is less than or equal to 0, the function is continuous, the first derivative is continuous, the second derivative is discontinuous, and the smoothness is poor~
If the function is not smooth, that is, the higher derivative does not exist, then its Taylor expansion is very short, and the error in calculating the value of the function is large. This is the practical significance. It is also the same for differential and integral. Taylor formula has differential form and integral form, which are also available, The error of differential and integral will increase. This error is generated when calculating by computer. It's not like you calculate integral manually, because most of the calculators can't do it. They all have to use computer, so the smoother, the higher the derivative order, the better the calculation accuracy~

1+2-3+4-5.+2002-2003=?

1+2-3+4-5+…… +2002-2003
=1+(2-3)+(4-5)+(6-7)+…… +(2002-2003)
=1-1-1-…… -1
=-1000
Because from (2-3) + (4-5) At first, the following are all - 1-1-1 A total of (2003-1) △ 2 = 1001
1001 - 1 equals - 1001, plus the previous 1, the final result is - 1000

0.05 square decimeter = () square centimeter

5 square centimeters

Given the point P (- 3,2), the coordinates of the point P symmetrical about the y-axis are (), the coordinates of the point P symmetrical about the x-axis are (), and the coordinates of the point P symmetrical about the origin are（

The coordinates of point P are (3,2) for Y-axis symmetry, (- 3, - 2) for X-axis symmetry and (3, - 2) for origin symmetry

To solve the problem, build a cylindrical reservoir with a bottom diameter of 10 meters and a depth of 2 meters. What is the floor area of the reservoir? What is the volume of the reservoir?
What is the volume of the pool?

Build a cylindrical reservoir with a bottom diameter of 10 meters and a depth of 2 meters. What is the floor area of the reservoir? What is the volume of the reservoir? How many cubic meters is the volume of the reservoir? The solution is: the floor area of the reservoir is actually the bottom area of the cylinder, so it is: 3.14 * (10 / 2) * (10 / 2) = = 78.5 square meters, so the reservoir accounts for

How to calculate 24 o'clock?

4 ÷ (1 - 5 ÷ 6)
Or 6 ^ (5 ^ - 4 - 1)

The volume of the geometry obtained by rotating the figure enclosed by parabola y = x2 / 2 and straight line y = 1 around the axis is equal to

Let the volume be v. first, we discuss the case of rotation around Y-axis v = ∫ [0 → √ 2] [π * X & sup2; dy] {note: here ∫ [0 → √ 2] denotes the definite integral with upper limit of √ 2 and lower limit of 0, the same below} v = π / 2 ∫ [0 → √ 2] [x & sup2; DX & sup2;] = π / 4 (2 & sup2; - 0) = π