It should be a formula for finding the root of a quadratic equation with one variable.
Quadratic equation is one of the great achievements of mankind in mathematical exploration. It was first put forward by Babylonians to solve the tax problem from 2000 BC to 1600 BC. Today, more than 4000 years later, the quadratic equation has been used to solve more diverse and complex mathematical application problems, and millions of people (especially students) are trying to engrave the formula of the quadratic equation in their minds.
Some people say that this is the formula for finding the root of bald head.
Have you ever been bothered by this radical?
This complex and unforgettable formula is to solve the quadratic equation ax? +bx+c=0。 When you were a junior high school student, solving equations began to bother you. You scratch your scalp to remember this invincible and complicated formula, and finally you have to deduce it again-the usual teaching methods are generally to use collocation to deduce the formula.
Mathematicians have spent centuries trying countless methods to solve quadratic equations, most of which are very complicated and even "anti-human". "Matching method" is a relatively simple and easy-to-understand derivation method widely used at present. This method is solved by "completing the square" rather than intuition.
The topic of quadratic equation has been put forward for more than 4000 years. Because of the complexity of its formula, it has also become a nightmare for algebra students for centuries.
The relationship between quadratic function and unary quadratic equation is as follows. Don't be confused.
1, unary quadratic equation
quadratic function
Special case of function value y=0.
Number of intersections between image and x-axis:
① When?
The image intersects the x axis at two points.
, in which
It's a quadratic equation with one variable.
Two of them. The distance between these two points.
② When?
There is only one intersection point between the image and the X axis;
③ When?
There is no intersection between the image and the x axis.
When a>0, the image falls above the X-axis, no matter whether X is any real number, there is y >；; 0;
When a<0, the image falls below the X-axis, regardless of whether X is any real number, there is Y.
2. The parabola image must intersect with the Y axis, and the coordinate of the intersection point is (0, c); ?
(1) when c >; 0, the intersection of parabola and Y axis is above X axis, that is, the ordinate of the intersection of parabola and Y axis is positive;
(2)? When c=0, the intersection of parabola and Y axis is the coordinate origin, that is, the ordinate of the intersection of parabola and Y axis is 0;
(3) When c < 0, the intersection of parabola and Y axis is below X axis, that is, the ordinate of the intersection of parabola and Y axis is negative.
To sum up, c determines the intersection position of parabola and y axis.
3.？ Summary of common solutions of quadratic function;
⑴? To find the coordinates of the intersection point between the image of quadratic function and X axis, it needs to be transformed into quadratic equation.
⑵? To find the maximum (minimum) value of quadratic function, it is necessary to transform quadratic function from general formula to vertex by collocation method;
⑶ Judging the quadratic function according to the position of the image.
The symbols of A, B and C in the middle, or the symbols of A, B and C in the quadratic function, should be combined with numbers and shapes to judge the position of the image;
⑷? The image of quadratic function is symmetrical about symmetry axis. Using this property, we can sum the coordinates of a point with known symmetry, or the coordinates of an intersection of axes, and then we can get the coordinates of another intersection from symmetry.