Jamel set a goal of selling 36 raffle tickets for a school fundraiser. He sold 125% of his goal. How many raffle tickets did Jamel sell?

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Benthega

18.12.2022

Mathematics

The c(t) equation, as you can see, is a quadratic equation, and thus its graph is a parabola, the leading term's coefficient is positive, so the parabola looks like the picture below

and the lowest point is at the vertex
c(t) reaches it's lowest point there

$\bf \textit{vertex of a parabola}\\ \quad \\

\begin{array}{lllccllll}
c(t)&=&1t^2&-10t&+76\\
&&\uparrow &\uparrow &\uparrow \\
&&a&b&c
\end{array} \qquad 
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)
\\\\\\\\
\textit{so, the cost } \boxed{{{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}}\textit{ will be the lowest at year }\boxed{-\cfrac{{{ b}}}{2{{ a}}}}$

Emily invested in google stock (in the thousands of dollars) between the years 2000- 2013. the value

Emily invested in google stock (in the thousands of dollars) between the years 2000- 2013. the value

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