A curve $C$ has equation $y = ax^3 + bx^2 + cx + d$, where $a$, $b$, $c$ and $d$ ar

Question

A curve $C$ has equation $y = ax^3 + bx^2 + cx + d$, where $a$, $b$, $c$ and $d$ are constants. The curve $C$ intersects the $y$-axis at the point $(0, 7)$ and passes through the points $(-2, -11)$, $(1, 1)$ and $(3, 19)$. Find the values of $a$, $b$, $c$ and $d$.[4] $C$ first undergoes a reflection about the $y$-axis and subsequently a translation of $1$ unit in the positive $y$-direction. Find the equation of the resulting curve.[2]

Accepted Answer

(i) $a=2,b=-3,c=-5,d=7$. (ii) $y=-2x^3-3x^2+5x+8$.

2024 MI PRU1 Q3

2024 MI PRU1 Q3

Solution:

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