Translate using $(x, y) \rightarrow(x, y+5)$, then reflect over the $y$-axis.

\begin{tabular}{|c|l|l|}
\hline Pre-image & Image & Final Image \\
\hline$R(-5,-2)$ & $R$ & $R$ \\
\hline$S(-1,-2)$ & $S$ & $S$ \\
\hline$T(-1,-4)$ & $T$ & $T$ \\
\hline$U(-5,-4)$ & $U$ & $U$ \\
\hline
\end{tabular}

y = a(x – h)2 + k , where (h, k) is the vertex;
in our case, P(x) = a ( x + b /2 a ) 2 − Δ/4a ;
a = -36; b = 900; c = -1584;
b/2a = 900/-72 = -12.5;
Δ = b 2 − 4ac = 810000 - 144*1584 = 581904 => -Δ/4a = 4041;
P(x) = (-36)(x - 12.5)^2 + 4041, where (12.5 , 4041) is the vertex;

Answered by crisforp | 2024-06-10

y = a(x – h)2 + k, where (h, k) is the vertex;
in our case, P(x) = a Δ/4a ;
a = -36; b = 900; c = -1584;
b/2a = 900/-72 = -12.5;
Δ = 4ac = 810000 - 144*1584 = 581904 => -Δ/4a = 4041;
P(x) = (-36)(x - 12.5)^2 + 4041, where (12.5 , 4041) is the vertex; ;

Answered by samanthareynee10 | 2024-06-12

The standard vertex form of the polynomial P ( x ) = − 36 x 2 + 900 x − 1584 is P ( x ) = − 36 ( x − 12.5 ) 2 + 4041 , with the vertex at ( 12.5 , 4041 ) .
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Answered by crisforp | 2024-12-24