Question

Find the x-intercepts of the parabola with vertex (6,27) and y-intercept (0,-81). Write your answer in this form (x1,y1),(x2,y2). If necessary, round to the nearest hundredth

Answer 1

you know how to put this in " vertex form" as \[y=a(x-h)^2+k\]?

Answer 2

It tells me use this formula: (y-k)=a(x-h)^2

Answer 3

ok same thing really

Answer 4

put in \(h=6, k=27\) leave the \(a\) as an \(a\) we will find it in a second

Answer 5

write it, let me check, then we can find \(a\) and finally we can solve

Answer 6

all i have then is: (y-6)=a(x-27)^2

Answer 7

yes, now to find \(a\)

Answer 8

But what do i do with y? that has to have a number for it

Answer 9

And what is x?

Answer 10

oh wait, it is wrong

Answer 11

we got the x and y backwards here \((y-6)=a(x-27)^2 \) it should have been \[(y-27)=a(x-6)^2 \]

Answer 12

I have 2 more questions to answer that i might need help on

Answer 13

we are not done with this one yet
now we need to find \(a\)

Answer 14

put \(x=0,y=-81\) and solve \[-81-27=a(0-6)^2\] for (a\)

Answer 15

so then from the y intercept i get (-81-27)=a(0-6)^2

Answer 16

right, solve for \(a\) let me know when you get it

Answer 17

-3=a

Answer 18

ok so now we have our parabola nailed down
it is \[y-27=-3(x-6)^2\]

Answer 19

i would prefer it looked like \[y=-3(x-3)^2+27\] so now we can set \(y=0\) and solve for \(x\) to finish the question

Answer 20

ok typo there \[y=-3(x-6)^2+27\]

Answer 21

or just leave it as \(y-27=-3(x-6)^2\) put \(y=0\) solve \[-27=-3(x-6)^2\]

Answer 22

you know how to do that?

Answer 23

so i would get y=-3x^2-6x^2 correct?

Answer 24

no

Answer 25

could you show me

Answer 26

\[-27=-3(x-6)^2\] divide both sides by \(-3\) first
then what do you get?

Answer 27

9=(x-6)^2

Answer 28

ok now take the square root of both sides
don't forget the \(\pm\) you are going to get two answers

Answer 29

9=x^2*6^2

Answer 30

then divide it all by 9?

Answer 31

hmm o

Answer 32

not square, take the square root

Answer 33

9 has two square roots, a positive one and negative one

Answer 34

yeah 3 and -3

Answer 35

k so from \[9=(x-6)^2\] we get two equations \[x-6=-3\\
x-6=3\]

Answer 36

add 6 to both sides to get your two answers

Answer 37

x=3
x=9

Answer 38

yes, final answers \[(3,0), (9,0)\]

Answer 39

It was right thanks! could you help me out on my other 2 questions that are the same thing.

Answer 40

sure post in a new thread, this one is gettting long