Question

Given three points of a quadratic function, find the equation that defines the function: (-2, 20)(0, -2)(1, -4)

Answer 1

`y=3x^2-5x-2`

Explanation:

Let the quadratic function be

`y=ax^2+bx+c`

The given points must satisfy this function;

Substitute
`(-2,20)`.

`20=4a-2b+c..(1)`

Substitute (0,-2)

`c=-2...(2)`

Substitute (1,-4);

`-4=a+b+c...(3)`

Put equation (2) into equation (1)

`20=4a-2b+-2`

`4a-2b=22`

`2a-b=11...(4)`

Put equation (2) into equation (3)

`-4=a+b-2...(3)`

`a+b=-2...(5)`

Add equation (4) and (5)

`3a=9`

Divide both sides by 3

`a=3`

Put a=3 in equation 5.

`3+b=-2`

`b=-2-3`

`b=-5`

The quadratic function is;

`y=3x^2-5x-2`