The function f(x) = −x2 + 28x − 192 models the hourly profit, in dollars, a shop makes for selling sodas, where x is the number of sodas sold and f(x) is the amount of profit.

Part A: Determine the vertex. What does this calculation mean in the context of the problem?

Part B: Determine the x-intercepts. What do these values mean in the context of the problem?

Question

The function f(x) = −x2 + 28x − 192 models the hourly profit, in dollars, a shop makes for selling sodas, where x is the number of sodas sold and f(x) is the amount of profit.

Part A: Determine the vertex. What does this calculation mean in the context of the problem?

Part B: Determine the x-intercepts. What do these values mean in the context of the problem?

jhonyy9 · Answer

A. do you know the way how you find the vertex of a quadratic ?

jhonyy9 · Answer

vertex (h,k)

$$h = - \frac{ b }{ 2a }$$

k = f(h)

angelcook2007 · Answer

what does that mean?

Extrinix · Answer

$h=-\dfrac{\color{lime}{b}}{2\color{cyan}{a}}$ is the equation to find the `x-coordinate` of a quadratic equation, a quadratic equation looks like this:

$\color{cyan}{a}\color{tomato}{x}^2+\color{lime}{b}\color{tomato}{x}+\color{yellow}{c}=0$

From your equation find $a~b$ and $c$

$\color{cyan}{-1}\color{tomato}{x}^2+\color{lime}{28}\color{tomato}{x}-\color{yellow}{192}=f(x)$

$\color{cyan}{a}=-1$
$\color{lime}{b}=28$
$\color{yellow}{c}=-192$

Plug it into or equation
$h=-\dfrac{\color{lime}{28}}{2\color{cyan}{-1}}$

Now just solve that and you'll have your answer.

angelcook2007 · Answer

wait, what happened to 192

angelcook2007 · Answer

-192 i meant