The axis of symmetry of the parabola y = ax ^ 2 + BX + C is x = 2, passing through (0,4) and (5,9) Write down the whole process

The axis of symmetry of the parabola y = ax ^ 2 + BX + C is x = 2, passing through (0,4) and (5,9) Write down the whole process

∵ parabola y = ax ^ 2 + BX + C over (0,4) and (5,9)
We substitute (0,4) and (5,9) into the parabola y = ax ^ 2 + BX + C to get
c=4
25a+5b+c=9 （1）
And because the axis of symmetry is x = 2
∴-b/2a=2 （2）
The solution of simultaneous (1) (2) is a = 1, B = - 4
Parabolic analytic formula y = x ^ 2-4x + 4
We look forward to your adoption

There are infinitely many optimal solutions for P (x, y) to move z = ax + y within and on the boundary of △ ABC
In △ ABC, if the three vertices are a (2,4) B (- 1,2), C (1,0), and the point P (x, y) moves inside and on the boundary of △ ABC, there are infinitely many optimal solutions for the maximum value of the objective function z = ax + y?

Kab=2/3,
Kbc=-1
Kca=4
Because there are infinitely many optimal solutions, the maximum value of Z = ax + y must coincide with the line AB or BC or ca,
Note that a is the opposite of the slope of the target line, and the target line must be moved up as much as possible (because the coefficient of Y is positive 1),
So a = - 2 / 3

It is known that the coordinates of two vertices a and B of triangle ABC are a (0,0), B (0,6), and vertex C moves on the curve y = x ^ 2 + 3,
Find the trajectory equation of triangle ABC center of gravity g? There must be specific steps~

Let C (x1, Y1); △ ABC's center of gravity H (x, y) ∵ C move on the curve y = x ^ 2 + 3 ∵ Y1 = X1 ^ 2 + 3 --- - (1) according to the triangle center of gravity coordinate formula: x = (0 + 6 + x1) / 3 = (6 + x1) / 3: X1 = 3x-6, y = (0 + 0 + Y1) / 3: Y1 = 3Y, take x1, Y1 into (1) formula: 3Y = (3x-6)

Given that a parabola intersects with X-axis at points a (- 2,0), B (4,0), and the ordinate of vertex C is 3, find the functional relation of parabola

Let the parabola equation be y = ax & # 178; + BX + C, and the abscissa of the parabola vertex be (- 2 + 4) / 2 = 1. Then C (1,3) substitutes a, B, C into the equation to obtain 4a-2b + C = 0, 16a + 4B + C = 0A + B + C = 3, solves the system of linear equations of three variables to obtain a = - 1 / 3, B = 2 / 3, C = 8 / 3, and substitutes it into the system of equations to obtain the functional equation y = - 1 / 3x & # 178; + 2 / 3x + 8 / 3