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do you know how to do this?
the x-intercept means y = 0 f(x) = 0 f(x) = profit maximum value = highest y value = highest profit
so x-intercept means theres 0 profit?
vertex is at 3, 120 so when x = 3 y = 120 3 pens maximum profit $120
ok and what about the increasing intervals?
question is asking how does y change as x changes
the more pens sold the higher the profit?
but aren't they asking for the intervals where the function is increasing and decreasing
up to the limit of 3 maximum so x 0 to 3 increase
x more than 3 profit decrease
x more than 3 profit decrease ?
look at the graph
now part B
wait but what does the sale an profit represent when it increases and decreases
change in y divided by change in x f(5) - f(3) divided by (5-3)
but what does the sale an profit represent when it increases and decreases
but last question
what is the equation for the graph?
yes you tell me
i don't know how to make an equation for it
ohh ok one second
how do i find a?
@triciaal how do i find a??
@ganeshie8 can u plz help
all i need is the equation and i don't know how to get to it @welshfella
equation for the graph can be written as f(x) = a(x - 3)^2 + 120 because the vertex is at (3,120) and a is a constant to be found
yes i did that too but i don't know ow to find a
f(x)=(x-0)(x-6)=0 is the equation?
the zeroes of the equation are x=0 and x = 6 so we can plug these into f(x) = a(x -3)^2 + 120 0 = (-3)^2 a + 120
i don't need the zeroes though, i only need the equation itself and thats it
f(x)=(x-3)^2+120 is this the equation
well if you find the value of a you'll get the equation
no - you need to find a
AHH whats a?!?!?
0 = 9 a + 120 a = ?
f(x) = a(x -3)^2 + 120
yea so we have f(x) -13.333(x - 3)^2 + 120
ok thank you so much!!!!
@welshfella can u give @triciaal a medal for me
you are welcome