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
MATH HELP ASAP - PLEASE. 1. A frog jumps from a rock to the shore of a pond. Its...
MATH - A FROG JUMPS A DISTANCE OF 25CM ON EACH JUMP.IF THE FROG JUMPS 6 TIMES ,...
pre-calc - path of a frogs leap: a frog leaps from a box 3 feet high and lands 4...
5th grade math - Three frogs had a race on a 1000 chart. Freaky Frog took 30 ...
physics (fluid mechanics: buoyant forces) - A frog in a hemispherical pod just ...
Physics - A frog with a mass of .14kg jumps by extending its legs 13.5cm, ...
Math - a Frog is at the bottom of a 21 foot well. The frog jumps up 4 feet, and ...
maths-perimeter - A circular pond has a 95cm wide foot path along the edge.A man...
Alg 1 - Landon is standing in a hole that is 6.5 ft deep. He throws a rock and ...
Physics - A frog is jumping around its pond. At some time t , the frog is in mid...