Algorithm of symmetry axis: for quadratic function y=ax? +bx+c, whose symmetry axis is the straight line x=-b/2a, and because y=-x? +3ax-2, so the symmetry axis is x=(-3a)/(-2)=3a/2.

Problem solving process: y=-x? +3ax-2=-(x？ -3ax)-2=-(x？ -3ax+9/4a？ )+9/4a？ -2=-(x-3/2a)？ +9/4a？ -2。 The symmetry axis of quadratic function refers to the straight line where the independent variable X is located when the quadratic function has the maximum value. This straight line is called the symmetry axis of the function.

Extended data:

The steps to find the symmetry axis are as follows:

y=ax^2+bx+c (a≠0)

1, when △≥0, x1+x 2 =-b/ax1= x 2, and the symmetry axis x=-b/2a.

2. When △ < 0, a> is 0, y>0, a<y < 0；; 0, y≠0, ax 2+bx+c-y = 0 △≥ 0, so the symmetry axis x=-b/2a.

Y becomes the opposite number and X remains unchanged, so Y = A (-X) 2+B (-X)+C, that is, Y = AX 2-BX+C.

When all the values are brought into the image, you will find a line that bisects them symmetrically, and this line is the symmetry axis of the function.

References:

Baidu Encyclopedia-Function Symmetry Axis