Word Problem

[strawbarri]

A movie theatre sells tickets for $8.50 each. The manager is considering raising the prices but knows that for every 50 cents the price is raised, 20 fewer people go to the movies. The equation R= -40c^2 + 84c describes the relationship between the cost of tickets, c dollars, and the amount of revenue, R dollars, that the theatre makes. What price should the theatre charge to maximize revenue?

Thanks !

 

[strawbarri]

I know I have to find the vertex algebraically, but Im not sure how to go about finding the vertex because a is a negative. I want to factor by 4 but does that mean it would be -10(c^2.... or would it be 10(-c^2...
Thanks!

 

[Deleted member 4993]

A movie theatre sells tickets for $8.50 each. The manager is considering raising the prices but knows that for every 50 cents the price is raised, 20 fewer people go to the movies. The equation R= -40c^2 + 84c describes the relationship between the cost of tickets, c dollars, and the amount of revenue, R dollars, that the theatre makes. What price should the theatre charge to maximize revenue?

Thanks !

If the equation of the parabolsa was:

y = Ax^2 + Bx + C

What would be the co-ordinates of the vertex?

 

[strawbarri]

Doesn't it have to be in vertex form to find the coordinates?

 

[Mrspi]

Doesn't it have to be in vertex form to find the coordinates?

No, it doesn't.

If you have the equation of a parabola in the form

y = ax^2 + bx + c

the x-coordinate of the vertex is -b/2a.

Once you know the x-coordinate of the vertex, you can substitute that value for x in the equation and find the y-value there.