Answer:
The required quadratic function that contain the points is
Step-by-step explanation:
Given : Points (-1,2), (0,-1) and (2,5).
To find : Formulate the quadratic function that contains the points ?
Solution :
The quadratic equation is in the form
![y=ax^2+bx+c](https://tex.z-dn.net/?f=y%3Dax%5E2%2Bbx%2Bc)
Substituting all the points and then solve the equation form.
Put (-1,2) i.e. x=-1 and y=2
......(1)
Put (0,-1) i.e. x=0 and y=-1
......(2)
Put (2,5) i.e. x=2 and y=5
......(3)
Substitute the value of c in equation (1) and (3),
We get,
In equation (1),
......(4)
In equation (3),
![5=4a+2b-1](https://tex.z-dn.net/?f=5%3D4a%2B2b-1)
![4a+2b=6](https://tex.z-dn.net/?f=4a%2B2b%3D6)
......(5)
Solving equation (4) and (5),
Add both equations,
![a-b+2a+b=3+3](https://tex.z-dn.net/?f=a-b%2B2a%2Bb%3D3%2B3)
![3a=6](https://tex.z-dn.net/?f=3a%3D6)
![a=2](https://tex.z-dn.net/?f=a%3D2)
Substitute in equation (4),
So, we get a=2 , b=-1 and c=-1
Substitute all in general formula of quadratic equation,
![y=ax^2+bx+c](https://tex.z-dn.net/?f=y%3Dax%5E2%2Bbx%2Bc)
![y=2x^2-x-1](https://tex.z-dn.net/?f=y%3D2x%5E2-x-1)
Therefore, The required quadratic function that contain the points is ![y=2x^2-x-1](https://tex.z-dn.net/?f=y%3D2x%5E2-x-1)