For example: y = (x+ 1) 2, then the symmetry axis is x=- 1, and the interval is a < x & lta+3. Compare the relationships between a and-1 and A+3 and-1 respectively: If a ≥-/.
Second, the determination of the axial motion interval: compare the position relationship between the symmetry axis and the end point of the interval, and judge the range of Y according to the monotonicity of the function.
For example, the interval range is -2.
The minimum value of the interval y = x 2+2ax+a 2 of the fixed axis is 1, so find a.
The minimum value of the fixed axis dynamic interval y = x 2+3x+4 in the interval [m, m+ 1] is 3, and m is found.
Extended data:
Axisymmetric graphics: line segment, angle, isosceles triangle, equilateral triangle, diamond, rectangle, square, isosceles trapezoid, circle, hyperbola (with two symmetry axes), ellipse (with two symmetry axes), parabola (with one symmetry axis), etc.
Number of symmetry axes: an angle has a symmetry axis, that is, the angle bisector of the angle; The isosceles triangle has an axis of symmetry, which is the median vertical line of the base; An equilateral triangle has three axes of symmetry, that is, the median vertical lines on three sides; A diamond has two symmetry axes, which are straight lines where two diagonals are located, and a rectangle has two symmetry axes, which are straight lines between two groups of opposite sides.
Centrally symmetric figures: line segments, parallelograms, diamonds, rectangles, squares, circles, etc.
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