The general formula of quadratic function is: y=ax? +bx+c (a≠0).
The highest order of a quadratic function must be quadratic, and the image of a quadratic function is a parabola whose symmetry axis is parallel or coincident with the Y axis.
Vertex of quadratic function: y=a(x-h)? The coordinate of +k vertex is (h, k)
Intersection point of quadratic function: y=a(x-x? )(x-x？ ) function and image intersect at (x? 0) and (x? ,0)
The image relationship of the general formula of quadratic function is y=ax? +bx+c(a≠0).
Relationship between a, b and c values and images
A>0, parabolic opening upward; A<0, parabolic opening downward.
When the parabola symmetry axis is on the left side of the Y axis, the symbols of A and B are the same, and when the parabola symmetry axis is on the right side of the Y axis, the symbols of A and B are different.
C>0, the intersection of parabola and Y axis is above X axis; C<0, the intersection of parabola and Y axis is below X axis.
When a=0, this image is a linear function.
When b=0, the vertex of the parabola is on the Y axis.
When c=0, the parabola is on the x axis.
When the parabola symmetry axis is on the left side of the Y axis, the symbols of A and B are the same, and when the parabola symmetry axis is on the right side of the Y axis, the symbols of A and B are different.
The formula of translation law of quadratic function is left plus right minus, addition and subtraction.
It means that when a quadratic function is written like this:
y=a(x+b)？ +c, just put y=ax? The function image of is converted according to the following rules.
( 1)b & gt； 0, the image moves to the left by b units (plus the left).
(2)b & lt； 0, the image moves b units to the right (minus the right side).
(3)c & gt； 0, the image moves up by c units (positive).
(4)c & lt； 0, the image moves down by c units (minus sign).