The quadratic function contains the points (-1,1), (0,-2), and (2,4) is [tex]y=2x^{2} -x -2[/tex]
The general equation of a quadratic equation is given by
[tex]y=ax^{2} +bx +c[/tex]......equation(1)
Now, the quadratic function contains the points (-1,1), (0,-2), and (2,4).
Putting these values in the quadratic equation,
Putting x = -1 and y = 1 in the equation, we have
1 = a(-1^2) +b(-1) +c
1 = a -b +c ......equation (2)
Putting x = 0 and y = -2 in the equation, we have
-2 = a(0) +b(0) +c
c = -2
Putting x = 2 and y = 4 in the equation, we have
4 = a(2^2) +b(2) + (-2)
4 = 4a +2b -2
2 = 2a + b -1
2 +1 = 2a + b
2a + b = 3
b = 3 -2a
Now, putting b = 3 - 2a and c = -2 in equation (2), we have
1 = a - (3 -2a) + (-2)
1 + 2 = a -3 +2a
3 + 3 = 3a
6 = 3a
a = 6/3 = 2
Now, b = 3 - 2*2 = 3 - 4 = -1
Thus, a = 2, b = -1 and c = -2
Putting these values in the general equation, we get
[tex]y=2x^{2} -x -2[/tex]
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