anonymous
  • anonymous
find coordinates of x/ y intercept and max or mini point on the grapg of these quad fuction. show answer by obtaining reasoing with sumbolic forms help: 9a ) f(x)=x(7-x) d) f(x)=-(x-3)(x+5) g) f(x)=2(x-3)(x-8)
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
you at least have the x,y intercepts?
anonymous
  • anonymous
i got nothing i got no idea how to do this
anonymous
  • anonymous
let's find those first.

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More answers

anonymous
  • anonymous
ok
apoorvk
  • apoorvk
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!
anonymous
  • anonymous
write it out pelase
anonymous
  • anonymous
finding the y-intercept is easy. make x=0 and evaluate each function.
phi
  • phi
we went through the 2nd equation in quite a bit of detail.
anonymous
  • anonymous
so for a it would be written f(0)=0(7-0)
anonymous
  • anonymous
phi internet stopped working so lost everything we did
anonymous
  • anonymous
ok, do the same for the other two...
anonymous
  • anonymous
forget that. let's just work on one function first.
anonymous
  • anonymous
oaky
anonymous
  • anonymous
this quadratic function opens up so it will have a.... (max/min)
anonymous
  • anonymous
ok
anonymous
  • anonymous
can you answer? max or min?
anonymous
  • anonymous
no
anonymous
  • anonymous
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.
anonymous
  • anonymous
ok
anonymous
  • anonymous
does it open upward or downard?
anonymous
  • anonymous
up?
phi
  • phi
This is going to be a frown shape. So it will have a maximum peak.
anonymous
  • anonymous
ok
phi
  • phi
Can you find the y intercept? f(0)=0(7-0)
anonymous
  • anonymous
would it be 0
phi
  • phi
That means multiply 0 times 7
anonymous
  • anonymous
its o
phi
  • phi
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
anonymous
  • anonymous
0
anonymous
  • anonymous
and 7
phi
  • phi
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
anonymous
  • anonymous
3.5
anonymous
  • anonymous
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
phi
  • phi
now to finish, find what the f(3.5) value is: f(x)=x(7-x) f(3.5) = 3.5*(7-3.5)
anonymous
  • anonymous
how to solve that
phi
  • phi
first do (7-3.5)=?
anonymous
  • anonymous
3.5
phi
  • phi
now multiply 3.5*(7-3.5) = 3.5 * 3.5 =
anonymous
  • anonymous
igot a werid number
anonymous
  • anonymous
is it 12.25
anonymous
  • anonymous
?
phi
  • phi
|dw:1332536502504:dw|
phi
  • phi
nothing wrong with 12.25
anonymous
  • anonymous
ok
phi
  • phi
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)
anonymous
  • anonymous
is that the answer for a?
phi
  • phi
yes. I hope you wrote it all down.
anonymous
  • anonymous
yes lets do g?
phi
  • phi
f(x)=2(x-3)(x-8) what is the y-intercept? (find f(0) , replace x with 0)
anonymous
  • anonymous
-3 and -8 when i do 0-3 and 0-8
phi
  • phi
yes, but you have to multiply all three numbers now.
anonymous
  • anonymous
48
anonymous
  • anonymous
?
phi
  • phi
yes the y-intercept is 48 now find the x-intercepts f(x)=2(x-3)(x-8) do you remember how?
anonymous
  • anonymous
how to do that
anonymous
  • anonymous
put x as 48
phi
  • phi
no. take notes: to find the x-intercept, find where f(x)= 0 that means find where 2(x-3)(x-8)=0
phi
  • phi
what x makes it zero?
anonymous
  • anonymous
3 nd 8
phi
  • phi
now find the x value where it peaks. Remember how?
anonymous
  • anonymous
ddont remember
phi
  • phi
find the average of the x-intercepts. add together and divide by 2
anonymous
  • anonymous
is it 5.5
phi
  • phi
yes. now find the peak value y(5.5)
anonymous
  • anonymous
how
phi
  • phi
replace x with 5.5 and do the arithmetic
phi
  • phi
f(x)=2(x-3)(x-8) <-- change the x to 5.5
anonymous
  • anonymous
is it -12.5
phi
  • phi
yes. Here is the graph |dw:1332537305940:dw|
phi
  • phi
Any more?
anonymous
  • anonymous
yes its iddferent tho
anonymous
  • anonymous
towrite rules for quadratic functions with grapgs that meet these conditons
anonymous
  • anonymous
x int (-2,0) and (-6,0) with graphy opening upward
anonymous
  • anonymous
can u help
phi
  • phi
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)
anonymous
  • anonymous
w
anonymous
  • anonymous
where did u come from
anonymous
  • anonymous
i mean were did 8 come from
phi
  • phi
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
phi
  • phi
That previous post was the last problem g you did.
anonymous
  • anonymous
wait so whats anser for g?
anonymous
  • anonymous
???
phi
  • phi
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)
anonymous
  • anonymous
okay can u help me with another three questions
anonymous
  • anonymous
we have to write rules for quadractic functions with graphs that meet the conitions
anonymous
  • anonymous
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)
phi
  • phi
b) x int (-2,0) (6,0) graph opening upward the answer is f(x)= (x-intercept1)(x-intercept2)
anonymous
  • anonymous
whats the rule?
phi
  • phi
replace intercept1 with the first intercept that they gave you. -2
anonymous
  • anonymous
how/ wat u mean
phi
  • phi
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)
phi
  • phi
It opens upwards because the number of minus signs in front of the x's is 0 (or even) it is a smile
anonymous
  • anonymous
ok
anonymous
  • anonymous
i got 0 and -8

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