Moderate -0.5 This is a straightforward C1 question requiring completion of the square or using the vertex form. Students need to apply the standard result that the minimum occurs at x = -a/2 and substitute to find both constants. It's slightly easier than average as it's a direct application of well-practiced techniques with no problem-solving insight required.
2. The curve \(C\) has the equation
$$y = x ^ { 2 } + a x + b$$
where \(a\) and \(b\) are constants.
Given that the minimum point of \(C\) has coordinates \(( - 2,5 )\), find the values of \(a\) and \(b\).
2. The curve $C$ has the equation
$$y = x ^ { 2 } + a x + b$$
where $a$ and $b$ are constants.
Given that the minimum point of $C$ has coordinates $( - 2,5 )$, find the values of $a$ and $b$.\\
\hfill \mbox{\textit{Edexcel C1 Q2 [4]}}