The 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? (5 points)

part b: determine the x-intercepts. what do these values mean in the context of the problem? (5 points)

The vertex is (25,361), the x intercepts are (6,0) and (44,0).

Step-by-step explanation:

Consider the provided function,

The standard equation of the quadratic equation is

And the vertex of the quadratic equation can be calculated as:

and k = f(h)

Part A:

By comparing the provided equation with the standard equation we can concluded that a = -1, b = 50 and c = -264

Now use the vertex formula and substitute the respective value in the formula that will give us the x coordinate of the vertex.

Now substitute h = 25 in the provided equation as shown:

Hence, the vertex is (25,361).

The provided equation has a negative x² coefficient that means it is a downward parabola having maximum at vertex (25,361) but there exist no minimum point.

In context of the problem: The profit will be maximum when the number of membership sold is 25.

Part B:

To determine the x intercept simply substitute f(x)=0 and solve for x.

Hence, the x intercepts are (6,0) and (44,0).

That means, there will be zero profit when the number of memberships sold are 6 or 44.

560

hope this : )

asdsad

step-by-step explanation: