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

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Answer 1 · 2017-06-28T07:34:15

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

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#