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olya-2409 [2.1K]
2 years ago
6

What is the vertex form of the quadratic equation represented on the table?

Mathematics
1 answer:
sergeinik [125]2 years ago
7 0

Check the picture below, so the parabola looks more or less like so, hmmm with a vertex at (-1 , -4), so, using those values from the table

~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}

\stackrel{vertex}{\stackrel{h}{-1}~~,~~\stackrel{k}{-4}}\qquad \implies y=a[x-(-1)]^2-4\implies y=a(x+1)^2-4 \\\\\\ \textit{we also know that} \begin{cases} x=2\\ y=14 \end{cases}\implies 14=a(2+1)^2-4\implies 18=9a \\\\\\ \cfrac{18}{9}=a\implies 2=a~\hspace{10em}\boxed{y=2(x+1)^2-4}

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Answer:

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Step-by-step explanation:

Deje que la cantidad inicial sea Andrés X, Braulio Y y Ciro Z

Luego, dado que cada uno pierde una apuesta en el orden presentado, tenemos;

Después de la primera apuesta, tenemos;

Andrés X-Y-Z, Braulio (Y + Y), Ciro (Z + Z)

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2 (X-Y-Z), 2Y - (X-Y-Z) - 2Z, 2Z + 2Z

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Multiplicamos las ecuaciones (2) por 7/2 y sumamos a la ecuación (3), tenemos;

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Restando la ecuación (4) de la ecuación (5) tenemos;

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De la ecuación (3), tenemos;

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Y₂ = 0.56

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