Determine the related quadratic function of the form \(y = ax^2 + bx + c\). Determine the constants \(a, b \text{ and } c\) by substituting any three data, for example \((0, 0), (25, 1.7) \text{ and } (30, 0)\) into the equation.
\(\text{(0,0)}\\ 0 = a(0)^2 + b(0) + c\\ c=0\\ \, \\ \text{(25,1.7)}\\ 1.7 = a(25)^2 + b(25) + c\\1.7 = 625a + 25b + c\\ \,\\ \text{(30,0)}\\ 0 = a(30)^2 + b(30) + c\\ 0 = 900a + 30b + c\)
Since \(c = 0\), the system of two linear equations in two variables is;
\(\begin{aligned} &1.7 = 625a + 25b \dots (1)\\ &\hspace{3.5mm}0 = 900a + 30b \dots(2)\\\\ &\text{From (2), } b=30a\dots(3) \end{aligned}\)
Substitute (3) into (1), we obtain \(a0.0136\). Substitute \(a0.0136\) into (3), we obtain \(b=0.408\).
\(\therefore y=−0.0136x^2 + 0.408x\dots(3)\)
Substitute \(x=15\) into (3), we obtain \(y=3.06\)
