OK. I think I have my head around most of this but for one question. I have plotted a graph with the quadratic equation tickets=-02x^2+12x+11.
My graph opens down and shows I will sell tickets for 60 days peaking at the vertex at 30 days where I sell 191 tickets.
Now I have to use the quadratic equation to determine the last day that tickets will be sold. (its the 60th day)I need to write my answer in terms of the number of days after ticket sales begin. I wish they could just use terms instead of words. How do I write the equation to answer the question?
I think you left out a decimal point in your equation. It should read
N = -0.2x^2 + 12x + 11
where N is the number sold on day x. That does result in a maximum of 191 on day 30.
If you assume that tickets stop being sold when N=0, then solve
-0.2x^2 + 12x + 11 = 0 for that day.
That's the same at
-x^2 + 60 x +55 = 0
The answer is x = 60.9 days
After 60 days, the number sold becomes negative, so the equation can no longer be valid.
Got it. Thank you
To find the last day that tickets will be sold, you need to determine the x-value where the graph intersects or touches the x-axis. In other words, you want to find the value of x when the y-value (number of tickets) is equal to 0.
To solve this, we can set the equation for tickets equal to 0:
-0.2x^2 + 12x + 11 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = -0.2, b = 12, and c = 11. Plugging these values into the formula, we get:
x = (-(12) ± √((12)^2 - 4(-0.2)(11))) / (2(-0.2))
Simplifying further:
x = (-(12) ± √(144 - (-8.8))) / (-0.4)
x = (-(12) ± √(144 + 8.8)) / (-0.4)
x = (-(12) ± √(152.8)) / (-0.4)
Now, we can calculate the values inside the square root:
x = (-(12) ± √(152.8)) / (-0.4)
x = (-(12) ± 12.36) / (-0.4)
There are two possible solutions for x since we have the ± sign:
x1 = (-(12) + 12.36) / (-0.4) ≈ 9
x2 = (-(12) - 12.36) / (-0.4) ≈ -18
Since we are interested in the number of days after ticket sales begin, we can discard the negative value (-18) as it does not make sense in this context.
Therefore, the last day that tickets will be sold is 9 days after ticket sales begin.