Solving three mathematical problems Find the expression of parabola passing through three points (- 2,0), (0, - 3), (2,2) If the intersection coordinates of the parabola and X axis are (- 2,0), (4,0) and pass (- 1,3), the expression of the parabola is determined If the vertex coordinates of a parabola are (- 2, - 3) and pass through points (1,4), find its expression

Solving three mathematical problems Find the expression of parabola passing through three points (- 2,0), (0, - 3), (2,2) If the intersection coordinates of the parabola and X axis are (- 2,0), (4,0) and pass (- 1,3), the expression of the parabola is determined If the vertex coordinates of a parabola are (- 2, - 3) and pass through points (1,4), find its expression

First question
Let the parabolic equation be y = ax ^ 2 + BX + C
According to the meaning of the title
4a-2b+c=0
c=-3
4a+2b+c=0
A = 3 / 4, B = 0, C = - 3 can be obtained by solving the above equations
So the parabolic equation is y = (3 / 4) x ^ 2-3
Second question
Let the parabolic equation be y = ax ^ 2 + BX + C
According to the meaning of the title
2a-2b+c=0
16a+4b+c=0
a-b+c=3
By solving the above equations, a = - 9 / 10, B = 21 / 10, C = 6
So the parabolic equation is y = (- 9 / 10) x ^ 2 + (21 / 10) x + 6
The third question
Let the parabolic equation be y = ax ^ 2 + BX + C
According to the meaning of the title
4a-2b+c=-3
a+b+c=4
-b/2a=-2
A = 7 / 9, B = 28 / 9, C = 1 / 9 can be obtained by solving the above equations
So the parabolic equation is y = (7 / 9) x ^ 2 + (28 / 9) x + 1 / 9
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