he function f(x) = −x2 + 50x − 264 models the profit, in dollars, a yoga studio makes for selling monthly memberships, where x is the number of memberships 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

he function f(x) = −x2 + 50x − 264 models the profit, in dollars, a yoga studio makes for selling monthly memberships, where x is the number of memberships 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?

Extrinix · Answer

$\color{yellow}{f(x)} = \color{cyan}{−1}x^2 + \color{lime}{50}x \color{tomato}{− 264}$
$\color{yellow}{f(x)} = \color{cyan}{a}x^2+~~~\color{lime}{b}x+~~\color{tomato}{c}$

So, we need to find the vertex of a quadratic, so:
Vertex = $\dfrac{-\color{lime}{b}}{2\color{cyan}{a}}$
So, plug these in:
Vertex = $\dfrac{-\color{lime}{50}}{2\color{cyan}{(-1)}}$

So it would be:
Vertex = $25$

And, vertex is the x-axis, so x would be 25.

angelcook2007 · Answer

@xhikari

angelcook2007 · Answer

I had to zoom in a bit and the vertex is 361

xhikari · Answer

yea the vertex as a whole is (25, 361) because when we graph it after inputting the x values we can see the highest point which is a maximum

xhikari · Answer

sry i took so long i was messaging someone

angelcook2007 · Answer

there's 2 x intercepts and that's the answer to B isn't it?