Given that the parabola passes through (4,0) and (- 2,0), and the maximum value is - (9 / 2), find the analytic expression of the function

Given that the parabola passes through (4,0) and (- 2,0), and the maximum value is - (9 / 2), find the analytic expression of the function

According to the meaning of the problem, we can assume that the analytic formula of the parabola is y = a (x-4) (x + 2), and when x = 1, y = - 9 / 2. Substituting it into the analytic formula, we get a = 1 / 2, so the analytic formula of the function is y = (x-4) (x + 2) / 2, that is, y = x ^ 2 / 2-3x-4

Given that the parabola passes through a [1,0], B [0, - 3], and the axis of symmetry is a straight line x = 2, find the analytic expression of the function

Parabola, and the axis of symmetry is x = 2
Let y = a (X-2) ^ + B ^ mean square
And because of a, B
Substitute a + B = 0
4a+b=-3
The solution is a = - 1, B = 1
So the analytic formula y = - (X-2) ^ + 1 = - x ^ + 4x-3

If the shape of a parabola is the same as that of the parabola y = - x ^ 2 + 2, and the axis of symmetry is x = 2, then the analytic expression of the parabola function is?

Move two units to the right and move up and down arbitrarily, that is y = - (X-2) ^ 2 + C (where C is any constant)