2016 H2 Mathematics Paper 1 Question 3

Graphs and Transformations

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(0,0)↓(x−l)4(l,0)↓k(x−l)4(l,0)↓k(x−1)4+m(l,m)\begin{gather*} (0,0) \\ \downarrow &(x-l)^4 \\ (l, 0) \\ \downarrow & k(x-l)^4 \\ (l, 0) \\ \downarrow & k(x-1)^4 + m \\ (l, m) \\ \end{gather*}
l=a  ■m=b  ■\begin{align*} l &= a \; \blacksquare \\ m &= b \; \blacksquare \end{align*}
Since the curve passes through (0,c),{(0, c),}
c=k(0−l)4+m=kl4+m=ka4+bk=c−ba4  ■\begin{align*} c &= k(0-l)^4 + m \\ &= k l^4 + m \\ &= k a^4 + b \\ k &= \frac{c-b}{a^4} \; \blacksquare \end{align*}