How do you write the quadratic function in standard form given points (1,2), (3,4), (6,-8)?
1 Answer
Dec 21, 2016
#y= -x^2+5x-2#
Explanation:
The Three points are
From this we can find the quadratic function in the form
#y=ax^2+bx+c#
We have to find
Let us generate three equations using the three points and the formula.
#a(1)^2+b(1)+c=2#
#a+b+c=2# ____(1)
#a(3)^2+b(3)+c=4#
#9a+3b+c=4# ------------------------------(2)
#a(6)^2+b(6)+c=-8#
#36a+6b+c=-8# ------------------------(3)
Using Cramer's rule we can solve these three equations
#a+b+c=2# ____(1)
#9a+3b+c=4# ------------------------------(2)
#36a+6b+c=-8# ------------------------(3)
It is generated from my template which I developed in MSExcel
#a=x; b=y; c=z#
#a = -1#
#b= 5#
#c=-2#
Then the quadratic function is -
#y= -x^2+5x-2#
