Question 13: Consider the function \(g(x)=mx^2+n\), where \(m\) and \(n\) are constant numbers. If \(g(4)=20\) and \(g(0)=5\) , find the values of \(m\) and \(n\).
Solution:
\(g(x)=mx^2+n\)
\(g(4)=m(4)^2+n\)
\(g(4)=16m+n\)
\(16m+n=20\)\(\ \_\_\_\_\_\_\ (1)\)\(\quad \because g(4)=20\)
\(g(0)=m(0)^2+n\)
\(g(0)=n\)
\(n=5\)\(\quad \because g(0)=5\)
Put value of \(n\) in equation \((1)\), we have
\(16m+5=20\)
\(16m=20-5\)
\(16m=15\)
\(m=\frac{15}{16}\)