The vertex coordinate formula of quadratic function in junior middle school mathematics for quadratic function y = ax 2+bx+c,
Its vertex coordinates are (-b/2a, (4ac-b 2)/4a) Intersection point: y=a(x-x? )(x-x？ ) [only when it is related to the x axis A(x? , 0) and B(x? 0) parabola],
Where x 1, 2 =-b √ b 2-4ac,
Vertex: y = a (x-h) 2+k,
[Vertex P(h, k) of parabola],
General formula: y = ax 2+bx+c (a, b and c are constants, a≠0),
Note: Among the three forms of mutual transformation, there are the following relationships: h=-b/2a=(x? +x？ ) /2k = (4ac-b 2)/4a Intersection with X axis: X? ，x？ =(-b √b^2-4ac)/2a。
So the vertex coordinate formula of quadratic function is that the vertex coordinate is (-b/2a, 4ac-b2/4a).
When the intersection of the quadratic function image and the X axis is △ = B2-4ac >; 0, the function image has two intersections with the x axis.
When △=b2-4ac=0, the function image has only one intersection with the x axis.
When △ = B2-4ac
As the key knowledge points of quadratic function, the first coefficient B and the second coefficient a*** both determine the position of symmetry axis.
When a>0 has the same number as B (namely ab>0), the symmetry axis is on the left of Y axis; Because the axis of symmetry is on the left, the axis of symmetry is less than 0, which is -b/2a.
When a>0, when it is different from B (i.e. AB; 0, so b/2a should be less than 0, so a and b should have different signs.
It can be simply recorded as left and right differences, that is, when the numbers of A and B are the same (that is, AB >；; 0), the symmetry axis is on the left of the y axis; When a and b have different numbers (i.e. AB
In fact, b has its own geometric meaning: the value of the slope k of the resolution function (linear function) of the tangent of the quadratic function image at the intersection of the quadratic function image and the Y axis. It can be obtained by taking the derivative of quadratic function.