Determine the equation of the polynomial of degree two whose graph passes through the points (1,6), (2,6) and (3,2). Find y when x= -2

Answers (1)

Standard form of a polynomial of degree 2 is :y=a*x^2+b*x+c
As the points passes through the curve,

Point(1,6):
6 = a*(1)^2 + b*(1) + c
Rightarrow 6 = a+b+c

Point(2,6):
6 = a*(2)^2 + b*(2) + c
Rightarrow 6 = 4a+2b+c

Point(3,2):
2 = a*(3)^2 + b*(3) + c
Rightarrow 6 = 9a+3b+c

Solving the equations, we get
a = -2, b=6, c=2
So the polynomial is     y = -2*x^2 + 6*x + 2
when; x=-2, y = -2*(-2)^2+ 6*(-2) + 2 = -18

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