X=-b/(2a) can make y maximum or minimum.

1, when a>0, the parabolic opening is upward, y has the maximum value.

2. When a

Substituting x=-b/(2a) into the general formula of quadratic function can get the extreme value of y (this is a general practice).

Another method is the matching method.

Say y is y=(kx+b)*(kx+b)+h or y =-(kx+b) * (kx+b)+h.

When kx+b=0, it is obvious that the first one gets the minimum value and the second one gets the maximum value.

Extended data:

Number of intersections between parabola and x axis:

1、δ= b？ -4ac & gt； 0, parabola and x axis have two intersections.

2、δ= b？ When -4ac=0, the parabola has 1 intersections with the X axis.

3、δ= b？ -4ac & lt； 0, the parabola has no intersection with the x axis.

Importance of coefficient expression

A determines the opening direction and size of the parabola. When a >; 0, the parabola opens upwards; When a<0, the parabola opens downward.

B and a*** both determine the position of the axis of symmetry. When A and B have the same sign (namely ab>0), the symmetry axis is on the left of Y axis; When a and b have different numbers (i.e. AB

C determines the intersection of parabola and y axis. The parabola and the y axis intersect at (0, c).

Baidu Encyclopedia-Quadratic Function