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Complete set of vertex coordinate formulas of quadratic function in junior middle school mathematics
Derivation of vertex coordinate formula of quadratic function: general formula: y = ax 2+bx+c (a, b, c are constants, a ≠ 0); Vertex: y = a (x-h) 2+k, [the vertex of parabola P(h, k]; For the quadratic function y = ax 2+bx+c, its vertex coordinates are (-b/2a, (4ac-b 2)/4a).

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.