Question

Can someone show me the steps to solving this?
What is the range of the graph of y = –7(x – 1)2 + 2?

Answer 1

what do you understand by range??

Answer 2

Nothing :/ aha.

Answer 3

http://www4b.wolframalpha.com/Calculate/MSP/MSP6851a12heb41fia6178000034h0he53413dc61h?MSPStoreType=image/gif&s=14&w=290&h=130&cdf=RangeControl

you should do some research .. how it came
your range will be = [-inf, 2]

http://www4b.wolframalpha.com/Calculate/MSP/MSP6851a12heb41fia6178000034h0he53413dc61h?MSPStoreType=image/gif&s=14&w=290&h=130&cdf=RangeControl

Answer 4

So would that be y is equal to or less than 2 or y is greater than or equal to 2?

Answer 5

Could you explain the steps used to find that answer? I'm trying to understand everything.

Answer 6

less or equal to 2, guess why??

Answer 7

huh?

Answer 8

i thought you wanted to find out why??

Answer 9

oh yeah I do.

Answer 10

still need help?

Answer 11

Yes.

Answer 12

don't ever give medal until your problem is solved completely or you satisfy completely. OK.

Answer 13

as you required range of the given function. then you have to separate out the x. now do it your self. I am waiting for your answer until.

Answer 14

aha ohkay & how do you seperate the x?

Answer 15

Sorry, math is not my best subject.

Answer 16

your original equation is\[\large y=-7(x-1)^{2}+2\]\[\large y+2=-7(x-1)^{2}\]\[\large \frac{y+2}{-7}=(x-1)^{2}\]or write the equation as\[\large (x-1)^{2}= \frac {y+2}{-7}\]taking square root on both sides.\[\large x-1=\pm \sqrt{\frac{y+2}{-7}}\]\[\large x=1\pm \sqrt{\frac{y+2}{-7}}\]It is done now. you have separated x.

Answer 17

woah that's confusing aha.

Answer 18

which step is making you confuse? tell me i am here to satisfy you miss.

Answer 19

The second step. Where it turns into y+2 instead of just y.

Answer 20

oh... sorry sorry. it is y-2.

on right side, 2 has plus sign. when it moves on left side then its sign becomes -

so change in all steps that it is y-2 not y+2

Answer 21

with modification, y-2
\[\large x=1\pm \sqrt{\frac{y-2}{-7}}\]

Answer 22

Oh ohkay that makes more sense aha

Answer 23

now you got how we can separate x?
should we progress now?

Answer 24

Yes

Answer 25

ok you know the value in the square root must be always positive otherwise we get imaginary number. for example.
\[\large y=\sqrt{2}\]this exists.
while\[\large y=\sqrt{-2}\]doesn't exist.

do you know this?

Answer 26

Yes I do

Answer 27

ok so the inner term in the square root must be positive i.e. \[\large \frac{2-y}{7}>0\]is it?

Answer 28

no

Answer 29

so. if y<2 then the quantity becomes positive.
if y=0 then the quantity becomes positive.
if y>2 then quantity becomes negative and the square root will have - sign in it. so it will ne undefined.

so range would be.\[\large (-\infty,2]\]
and this range your function will define.

Answer 30

Oh ohkay thanks! :D

Answer 31

welcome.