The quadratic function $y=\left( A-C \right){{x}^{2}}+\left( 3B-2 \right)x+1$, where $A$, \

Question

The quadratic function $y=\left( A-C \right){{x}^{2}}+\left( 3B-2 \right)x+1$, where $A$, $B$ and $C$ are real numbers, is obtained by transforming the function $y=A{{x}^{2}}+Bx+C$ through the following sequence of transformations: Step 1: Translation of $5$ units in the negative $y$-axis direction; Step 2: Scaling parallel to the $x$-axis with scale factor $\frac{1}{2}$. Show that $4A+B+C=0$.[3]

Accepted Answer

$A=-2$, $B=2$, $C=6$, so $4A+B+C=0$

2015 CJC Promo Q8

2015 CJC Promo Q8

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