If the parabola intersects the x-axis at points (2,0), (3,0) and the y-axis at points (0, - 4), then the expression of the quadratic function is________________ .

If the parabola intersects the x-axis at points (2,0), (3,0) and the y-axis at points (0, - 4), then the expression of the quadratic function is________________ .

Y = - 2 / 3 · (X-2) · (x-3)
Or: y = - 2 / 3 of the square of X + 10 / 3 of the square of x-4

Given the intersection of parabola and X-axis at points a (- 2,0), B (4,0), and through (1,3), the expression of known function can be obtained

Because it intersects two points a and B with the x-axis, the axis of symmetry is 1, let the parabola be y = a (x-1) + B, and bring a and B into the system of equations. Because (1,3) leads to the system of equations, a = - 1 / 3, B = 3, so the parabola is y = - 1 / 3 (x-1) &# + 3

The vertex of parabola y = AX2 + BX + C is C (1,4), intersecting X-axis at point a (3,0), intersecting Y-axis at point D. find the expression of straight line ad
A (3,0) B (- 2,0) C (1,4) d (0, c) a < 0 b > 0 C > 0 axis of symmetry: straight line x = 1

In fact, it's not difficult to notice that if the analytic formula is y = ax * 2 + BX + C, the vertex coordinates of the quadratic function of one variable can be expressed as (- B / 2a, (4ac-b * 2) / 4A), so according to the meaning of the problem, we can get the equation system 1) - B / 2A = 12) (4ac-b * 2) / 4A = 43) by substituting the point a into the equation, we can get three simultaneous solutions

It is known that the parabola y = - x2 + (A-1) x + a intersects the Y axis at the point (0, 3). (1) find the value of a; (2) find the symmetry axis and vertex coordinates of the parabola; (3) when x takes what value, y has the maximum value? What is the maximum value? (4) When x takes what value, y decreases with the increase of X? (5) How to translate the parabola y = - x2 + (a + 1) x + A to make its vertex on the x-axis?

(1) Substituting the point (0, 3) into y = - x2 + (A-1) x + A, we get a = 3; (2) the analytical formula of parabola is y = - x2 + 2x + 3 = - (x-1) 2 + 4, so the axis of symmetry is a straight line x = 1, and the vertex coordinates are (1, 4); (3) when x = 1, y has a maximum value, and the maximum value is 4; (4) when x > 1, y decreases with the increase of X