Does the graph of this equation open up or down?

Tickets= -0.2x^2+12x+11

Describe what happens to the tickets sales as time passes?

The graph of this equation will open DOWNWARDS cause here a is -ve.

I think that increases at first and reach an optimum, then decreases. Must check it though. Do you know how to complete the square of a quadratic? While doing that mentally, I found that the curve (having a -ve coefficient for the x^2 has a maximum) has a center at the x-coordinate of 30 (or time 30), therefore meaning that it increases at first then reach an optimum and finally falls. Waiting for others to comfirm that.

Attachment 11277

Dude! It is obvious that a quadratic equation will always have a parabola type(not exact parabola) graph. We just have to find whether it opens up or down, its vertex, roots(points where it cuts the x axis) etc...

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Originally Posted by KLC1230

Describe what happens to the tickets sales as time passes?

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That was the question I replied. With the time axis, the -ve part of the x-axis is not concerned, as well as the -ve part of the y-axis, being the amount of tickets.

to make a perfect square of a quadratic, first make the co-efficient of x^2 equal to one, then add and subtract the square of the half of the co-efficient of x, then analyze the equation and you will find it is now easy to make it a perfect square!

That's what I did in case you didn't realise that. You will find the x-coordinate to be 30, as shown in your graph.

Unknown008! Could you please explain the concept behind the second part of the question?

I think first it will increase up to 30 and then decreases and we should only consider the first quadrant of the graph only! Am I right?

Well, if you like. Using a graph, and labelling the axes correctly, x-axis as time and y-axis as the number of ticket sales, you'll find that the number of ticket sales increases for the first 30 units (maybe seconds, minutes, hours, etc.) of time passed. After that, it decreases until it falls to zero.