Question

Find the equation of the quadratic passing through (0,0.24), (1,0.31) and (2,0.36) and complete the square for it. This is a quadratic modelling question.

Answer 1

Let the quadratic be f(x)=ax²+bx+c.

f(0)=0.24, so c=0.24.

f(1)=0.31=a+b+c=a+b+0.24, a+b=0.07.

f(2)=0.36=4a+2b+c=4a+2(0.07-a)+0.24=2a+0.38, 2a=0.36-0.38=-0.02, a=-0.01, so b=0.07+0.01=0.08.

f(x)=-0.01x²+0.08x+0.24.

To express this in the form a(x-h)²+k,

f(x)=0.24-0.01(x²-8x+16-16)=

0.24-0.01(x-4)²+0.16=0.40-0.01(x-4)².

f(x)=-0.01(x-4)² +  0.40.