Ijust need figuring out what numbers mean because i'm dumb.
this is the situation:
"when the taco truck charges $4 for a taco, it sells an average of 60 tacos in one day. with every $1 increase in the price of a taco, the number of tacos sold per day decreases by 7. the owner can calculate the daily revenue using the polynomial expression -7x^2 + 32x + 240, where x is the number of $1 increases in the taco price."

i need to know what the 32 is supposed to represent, and what the 240 represents.

f(x) = -7x² + 32x + 240

f(0)=240

Answer for 240:  The 240 is the revenue at the regular price, a $0 increase.   It comes from 60 tacos at $4 a pop.

When we add $1 to the price we sell 53 tacos, 7 fewer.

Our revenue is 5*53 = 265

That matches f(1):

f(1) = -7 + 32 + 240 = 265

Let's see how to figure out f(x),

f(0)=4(60)=240

f(1)=5(60-7) = 265

f(2) = 6(60-2(7)) = 276

So in general,

f(n) = (n+4)(60 - 7n)

f(n) = 60n - 7n² - 28n + 240

f(n) = -7n² + 32n + 240

We see the 32n comes from 60n, which is the amount of additional money if we still sold 60 tacos at the new price, less 28n, which is the amount of money we didn't get at the original price because we raised the price.

32 is $60, the original taco count times $1 , less $28, which is 7 fewer times the original price of $4.

x = 17

step-by-step explanation:

1st step: isolate x.

24 - 3x = -27

-24         -24

-3x   =   -51

2nd step: divide.

-3x     =   -51

  3             3

  x       =     17

hope this

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1