looks like you are studying quadratic function.
You should have learned a method to find the vertex of such a funtion
here is a quick way
for y = ax^2 + bx + c
the x of the vertex is -b/(2a)
so in your case
x = (-5/3)/(-5/32) = 32/3
sub back in to get
y = 80/9
y is your height,
x is your horizontal distance
2. let the number of $0.50 increases be n
profit = (12 + .5n)(220 - 10n)
expand to get a quadratic, repeat the method I showed you in #1
3. let the function be
y = a(x-7)^2 + 10 , in the usual vertex form
but (10,28) lies on it
so 28 = a(10-7)^2 + 10
solve for a, and you got it
For 2 I did the function and got n=-1. then i substitute it in and got 11.5 is that the answer? if so to which of the 2 questions?
You are right, n = -1
Since I defined n as the number of .50 "increases" we have to interpret that as a "decrease" of 50 cents.
you can verify this by making a chart
cost - number - profit
12.00 220 ---- 2640
12.50 210 ---- 2625
11.50 230 ---- 2645
11.00 240 ---- 2640
so the price should be $11.50, selling 230 of them for a maximum profit of $2645
btw, (11.5 , 2645) would be the vertex of your function
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