Question

Given three points (0,-4) (1,0) (2,2) how do you write a quadratic function in standard form with the points?

Answer 1

Quadratic function is `y=-x^2+5x-4`

Explanation:

Let the quadratic function be `y=ax^2+bx+c`.

As the function passes through points `(0,-4), (1,0)` and `(2,2)`, we have

`-4=a*0^2+b*0+c` or `c=-4`

now we may put `c=-4` in relations formed by other two points i.e.

`0=a*1^2+b*1-4` or `a+b=4` ...........(A)

and `2=a*2^2+b*2-4` or `4a+2b=6` or `2a+b=3` ...........(B)

Subtracting (A) from (B), we get

`a=3-4=-1`

and hence `b=4-a=4-(-1)=5`

and quadratic function is `y=-x^2+5x-4`