Moderate -0.8 This is a straightforward application of the factor theorem with a clear path to solution: write f(x) = a(x+4)(x-2)(x-4), expand, then use the y-intercept (0,16) to find a. The question requires only routine algebraic manipulation with no problem-solving insight needed, making it easier than average.
4.
\includegraphics[max width=\textwidth, alt={}, center]{fbe229f8-d390-487d-87fc-90edc50c3325-3_554_988_1153_486}
The figure above shows the graph of the curve with equation \(y = f ( x )\).
The curve crosses the \(x\) axis at the points \(( - 4,0 ) , ( 2,0 )\) and \(( 4,0 )\), and the \(y\) axis at the point \(( 0,16 )\).
Determine the equation of \(f ( x )\) in the form
$$f ( x ) \equiv a x ^ { 3 } + b x ^ { 2 } + c x + d$$
where \(a , b , c\) and \(d\) are constants.
4.\\
\includegraphics[max width=\textwidth, alt={}, center]{fbe229f8-d390-487d-87fc-90edc50c3325-3_554_988_1153_486}
The figure above shows the graph of the curve with equation $y = f ( x )$.
The curve crosses the $x$ axis at the points $( - 4,0 ) , ( 2,0 )$ and $( 4,0 )$, and the $y$ axis at the point $( 0,16 )$.
Determine the equation of $f ( x )$ in the form
$$f ( x ) \equiv a x ^ { 3 } + b x ^ { 2 } + c x + d$$
where $a , b , c$ and $d$ are constants.\\
\hfill \mbox{\textit{SPS SPS SM 2021 Q4 [5]}}