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you at least have the x,y intercepts?
i got nothing i got no idea how to do this
let's find those first.
make x=0 and the value of y will give y-intercept. conversely true for x-intercept. for maxima or minima, differentiate and equate the differential to 0. the values of x for which it's zero, gives point of maxima and minima!
write it out pelase
finding the y-intercept is easy. make x=0 and evaluate each function.
we went through the 2nd equation in quite a bit of detail.
so for a it would be written f(0)=0(7-0)
phi internet stopped working so lost everything we did
ok, do the same for the other two...
forget that. let's just work on one function first.
this quadratic function opens up so it will have a.... (max/min)
can you answer? max or min?
y = x(7-x) = 7x -7x^2. the coefficient of the x^2 term will tell you if it's opening upward or downward. If the number is positive, it opens upward. if negative, then downward.
does it open upward or downard?
This is going to be a frown shape. So it will have a maximum peak.
Can you find the y intercept? f(0)=0(7-0)
would it be 0
That means multiply 0 times 7
so you have the y-intercept. Now find the x-intercepts f(x)=x(7-x) what x values make this 0? x(7-x)=0
ok you have the y-intercept = 0, you have 2 x-intercepts 0 and 7 now find the x where the parabola peaks. It is half way between the 2 x intercepts add them together and divide by 2
dear take the second derivative of this function must be equal to zero, then if you get the positive answer then its minima and if you get the negative one then its maxima
now to finish, find what the f(3.5) value is: f(x)=x(7-x) f(3.5) = 3.5*(7-3.5)
how to solve that
first do (7-3.5)=?
now multiply 3.5*(7-3.5) = 3.5 * 3.5 =
igot a werid number
is it 12.25
nothing wrong with 12.25
so you finished that problem. now this one f(x)=2(x-3)(x-8) what is the y-intercept? (find f(0) , replace x with 0)
is that the answer for a?
yes. I hope you wrote it all down.
yes lets do g?
f(x)=2(x-3)(x-8) what is the y-intercept? (find f(0) , replace x with 0)
-3 and -8 when i do 0-3 and 0-8
yes, but you have to multiply all three numbers now.
yes the y-intercept is 48 now find the x-intercepts f(x)=2(x-3)(x-8) do you remember how?
how to do that
put x as 48
no. take notes: to find the x-intercept, find where f(x)= 0 that means find where 2(x-3)(x-8)=0
what x makes it zero?
3 nd 8
now find the x value where it peaks. Remember how?
find the average of the x-intercepts. add together and divide by 2
is it 5.5
yes. now find the peak value y(5.5)
replace x with 5.5 and do the arithmetic
f(x)=2(x-3)(x-8) <-- change the x to 5.5
is it -12.5
yes. Here is the graph |dw:1332537305940:dw|
yes its iddferent tho
towrite rules for quadratic functions with grapgs that meet these conditons
x int (-2,0) and (-6,0) with graphy opening upward
can u help
when we found the x-intercepts of to find the x-intercept, find where f(x)= 0 that means find where 2(x-3)(x-8)=0 we found x= 3 and x=8. So if we start with x=3 and x=8 we subtract: (x-3) and (x-8) and them multiply together (x-3)(x-8)
where did u come from
i mean were did 8 come from
with x int (-2,0) and (-6,0) with graphy opening upward the (-2,0) means x= -2 , y=0 (-6,0) means x=-6 , y= 0
That previous post was the last problem g you did.
wait so whats anser for g?
you already have the answer for g. I was explaining that if we "undo" problem g, it is like this new problem. the x-intercepts happen when you have (x-intercept1)(x-intercept2)
okay can u help me with another three questions
we have to write rules for quadractic functions with graphs that meet the conitions
b) x int (-2,0) (6,0) graph opening upward e) x int at (2,0) and (6,0) with max point at (4,2) f) x int at (-2,0) and (6,0) with y int at (0,-60)
b) x int (-2,0) (6,0) graph opening upward the answer is f(x)= (x-intercept1)(x-intercept2)
whats the rule?
replace intercept1 with the first intercept that they gave you. -2
how/ wat u mean
x int (-2,0) (6,0) graph opening upward this means f(x)= 0 when x= -2 or x= 6 so use the rule: f(x)= (x - -2)(x-6) (if you replace x with -2 or 6 f(x)=0 simplify: f(x)= (x+2)(x-6)
It opens upwards because the number of minus signs in front of the x's is 0 (or even) it is a smile
i got 0 and -8