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)

- anonymous

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- anonymous

you at least have the x,y intercepts?

- anonymous

i got nothing i got no idea how to do this

- anonymous

let's find those first.

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## More answers

- anonymous

ok

- 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

write it out pelase

- anonymous

finding the y-intercept is easy. make x=0 and evaluate each function.

- phi

we went through the 2nd equation in quite a bit of detail.

- anonymous

so for a it would be written f(0)=0(7-0)

- anonymous

phi internet stopped working so lost everything we did

- anonymous

ok, do the same for the other two...

- anonymous

forget that. let's just work on one function first.

- anonymous

oaky

- anonymous

this quadratic function opens up so it will have a.... (max/min)

- anonymous

ok

- anonymous

can you answer? max or min?

- anonymous

no

- 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

ok

- anonymous

does it open upward or downard?

- anonymous

up?

- phi

This is going to be a frown shape. So it will have a maximum peak.

- anonymous

ok

- phi

Can you find the y intercept?
f(0)=0(7-0)

- anonymous

would it be 0

- phi

That means multiply 0 times 7

- anonymous

its o

- 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

0

- anonymous

and 7

- 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

3.5

- 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

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

how to solve that

- phi

first do (7-3.5)=?

- anonymous

3.5

- phi

now multiply
3.5*(7-3.5) = 3.5 * 3.5 =

- anonymous

igot a werid number

- anonymous

is it 12.25

- anonymous

?

- phi

|dw:1332536502504:dw|

- phi

nothing wrong with 12.25

- anonymous

ok

- 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

is that the answer for a?

- phi

yes. I hope you wrote it all down.

- anonymous

yes lets do g?

- phi

f(x)=2(x-3)(x-8)
what is the y-intercept? (find f(0) , replace x with 0)

- anonymous

-3 and -8 when i do 0-3 and 0-8

- phi

yes, but you have to multiply all three numbers now.

- anonymous

48

- anonymous

?

- phi

yes the y-intercept is 48
now find the x-intercepts
f(x)=2(x-3)(x-8)
do you remember how?

- anonymous

how to do that

- anonymous

put x as 48

- 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

what x makes it zero?

- anonymous

3 nd 8

- phi

now find the x value where it peaks. Remember how?

- anonymous

ddont remember

- phi

find the average of the x-intercepts. add together and divide by 2

- anonymous

is it 5.5

- phi

yes. now find the peak value y(5.5)

- anonymous

how

- phi

replace x with 5.5 and do the arithmetic

- phi

f(x)=2(x-3)(x-8) <-- change the x to 5.5

- anonymous

is it -12.5

- phi

yes. Here is the graph
|dw:1332537305940:dw|

- phi

Any more?

- anonymous

yes
its iddferent tho

- anonymous

towrite rules for quadratic functions with grapgs that meet these conditons

- anonymous

x int (-2,0) and (-6,0) with graphy opening upward

- anonymous

can u help

- 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

w

- anonymous

where did u come from

- anonymous

i mean were did 8 come from

- 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

That previous post was the last problem g you did.

- anonymous

wait so whats anser for g?

- anonymous

???

- 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

okay
can u help me with another three questions

- anonymous

we have to write rules for quadractic functions with graphs that meet the conitions

- 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

b) x int (-2,0) (6,0) graph opening upward
the answer is f(x)= (x-intercept1)(x-intercept2)

- anonymous

whats the rule?

- phi

replace intercept1 with the first intercept that they gave you. -2

- anonymous

how/ wat u mean

- 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

It opens upwards because the number of minus signs in front of the x's is 0 (or even)
it is a smile

- anonymous

ok

- anonymous

i got 0 and -8

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