Question

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)

Answer 1

medal

Answer 2

\[f(x)=-x^2+50x-264 \\ \text{ factor } -1 \text{ from the first two terms } \\ f(x)=-(x^2-50x)-264 \\ \text{ now I'm going to leave a little space in the ( )} \\ \text{ this space will be the number we put into complete the square } \\ \text{ but whatever I add in } \\ \text{ I have to subtract out } \\ f(x)=-(x^2-50x+?)-264+? \\ \text{ notice I added in a zero } -?+?=0\]

Answer 3

now it is time to figure what number that ? should be

Answer 4

do you know how to complete the square?

Answer 5

kinda

Answer 6

okay so what number should the ? be

Answer 7

hint:
\[x^2+kx+(\frac{k}{2})^2 \text{ is equal to } (x+\frac{k}{2})^2 \]

Answer 8

2
?

Answer 9

am i right

Answer 10

hello?

Answer 11

hmm... how did you get that?

Answer 12

when you complete a square arent you suposed to add in a 2

Answer 13

did you read this?
\[x^2+kx+(\frac{k}{2})^2 \text{ is equal to } (x+\frac{k}{2})^2 \\ \]

Answer 14

\[x^2-50x+... \text{ is the same as } x^2+kx... \text{ when } k=-50 \\ x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2 \\ x^2-50x+...=(x+..)^2 \\ \]

Answer 15

I left those spaces for you
what number should be in place of first space, the space that has 3 dots in it