The root formula of quadratic function How did predecessors deduce the formula of root seeking? Who made this great feat? Does quadratic function have analytic formula or image first?

From the matching method to!
Descartes invented it!
First of all, there was an analytic formula. Then we invented the plane rectangular coordinates before we had the image

Find all the root formulas of quadratic function and all evolution root formulas, the more the better,

Solving quadratic function problems
We should master the change of three forms of quadratic function
(1) If we know the two intersections with X axis, we use the analytic formula of intersection, y = a (x-x1) (x-x2);
(2) If we know the symmetry axis, vertex, etc., and need to find the maximum and minimum value, we use the vertex formula y = a (X-H) ^ 2 + M
(3) For other cases, the general formula y = ax ^ 2 + BX + C is used

Calculating skills of root sign

You break down the number under the root sign into 4x___ Appearance, if can divide, continue to divide, in the square

If 2 is less than a and less than 3, what is the square formula and solution of the square of the root A-2 bracket minus the square of the root 3-A bracket

∵ 2 is less than a and less than 3
∴a-2＞0.3-a＞0
The square of the root A-2 bracket minus the square of the root 3-A bracket
=Ia-2I-I3-aI
=a-2-(3-a)
=2a-5

Look for a table whose root number is almost equal to several! It's similar to a table where root 2 equals 1.414 and root 3 equals 1.732,

Calculator is OK, ask what have what

Find the integral of (1-x) / (1 + x) under the radical sign

∫√[(1-x)/(1+x)]dx = ∫√[(1-x)^2 / (1-x^2)]dx = ∫(1-x) / √(1-x^2)dx= ∫1 / √(1-x^2)dx - ∫x / √(1-x^2)dx= arcsinx - 1/2∫1 / √(1-x^2)d(1-x^2)= arcsinx - √(1-x^2) + C

Use the transformation of multiplication formula to solve the following problem, given the root number 2015 + X + root sign 5 + x = 2, find the value of root number 2015 + X - root sign 5 + X

Because [root (2015 + x) + root (5 + x)] * [root (2015 + x) - root (5 + x)] = [root (2015 + x)] - square of [root (5 + x)] = (2015 + x) - (5 + x) = 2010, while root (2015 + x) + root (5 + x) = 2, so root (2015 + x) - root (5 + x) = 2010 / 2 = 1005

How to use absolute values when drawing functions on Geometer's Sketchpad

Version 5.0 is an example
1. "Data" → → click "calculate". In the dialog box, the word (function) will appear. If you click again, you will get [ABC], as shown in the figure:
2. If the method of drawing function image is similar .

One day, Li Xiaohu used the Geometer's Sketchpad to draw a picture. He first drew two parallel lines AB and CD, then drew a little e between the parallel lines, and then tied be and de (Fig. 1), he points point e with the left mouse button, and drags to get the figures as shown in Fig. 2, 3 and 4 respectively. At this moment, he suddenly thinks, is there any connection between the degrees of ∠ B, ∠ D and ∠ bed? Then, Xiao Hu finds out the relationship between the three angles by using the "measuring angle" and "calculation" functions of the Geometer's Sketchpad (1) Can you explore the quantitative relationship between ∠ B, ∠ D and ∠ bed in the graphs 1 ~ 4? (2) Please choose one of the four relationships to justify it

1、∠E=∠B+∠D
2、∠B+∠E+∠D=360
3、∠B+∠E=∠D
4、∠D+∠E=∠B

As shown in the figure, when technicians draw parallel lines with a "Ding" ruler, what is the mathematical basis

According to the theorem: two lines perpendicular to the same line are parallel

The root formula of quadratic function How did predecessors deduce the formula of root seeking? Who made this great feat? Does quadratic function have analytic formula or image first?