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anonymous
 5 years ago
the function f is defined for all real numbers x by f(x) = ax^2 + bx + c where a, b and c are constants and a is negative, in the xyplane, the x coordinate of the vertex of the parabola is y=f(x) is 1. if t is a number for which f(t) > f(0), which of the following (any or all) must be true?
1: 2 < t < 0
2: f(t) < f(2)
3: f(t) > f(1)
please help!
anonymous
 5 years ago
the function f is defined for all real numbers x by f(x) = ax^2 + bx + c where a, b and c are constants and a is negative, in the xyplane, the x coordinate of the vertex of the parabola is y=f(x) is 1. if t is a number for which f(t) > f(0), which of the following (any or all) must be true? 1: 2 < t < 0 2: f(t) < f(2) 3: f(t) > f(1) please help!

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myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0we know this parabola is oven downward because a is negative and the vertex is (1,k)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0f(t)=a(t+1)^2+k and f(0)=a(0+1)^2+k=a+k and f(t)>f(0) so we have a(t+1)^2+k=a+k

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so are you solving as a system here?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i solve that equation by using remedial algebra

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0subtract k on both sides

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0divide by a on both sides

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0square root both sides

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, i think i understand that. also, it says option 3 is true, can you help with that?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0lets see we gots to think I can't believe I could actually about the first one lol

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i have a question where i have equal sign, it should had been a greater than sign a(t+1)^2+k>a+k I don't know if you caught that or not

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, i assumed it was since the problem is dealing with inequality

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0okay cool im still thinking about 3

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i wonder what happens if we assume f(t)>f(1) and solve for t again im going to try

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0you said the last one is true?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0the interval (3,1) is not included in the first interval we got so i would think the 3rd one would be false unless i made a mistake somewhere

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right, but possibly the range works somehow? i have the harder time getting why option 3 works...

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0oh wait we have t>1 or t<3 not 3<t<1

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0oomg wait are you for sure number 1 is right? is it true or false?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0ok sqrt(x^2)=x, so we have sqrt((t+1)^2)>1 and sqrt((t+1)^2))<1 so we have t>0 or t<2 and for the last one we got t<3 or t>1 which are included in that interval so number 3 is true and number 1 is false now what about number 2...

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0for the second one we get 2<t<0 but we said t>0 or t<2 so number 2 is false

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i get it. the only true one is number 3 the others are FALSE!

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0what do you think? any questions/

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i'm fixing to go to bed if you dont have any questions

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0I really don't want to leave if you have questions, but I'm sleepy and I don't know if I should wait or not

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i think i kind of get it, although i'm not sure where the absolute value comes in

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0sqrt(x^2)=x just think about it whats sqrt((3)^2) and is equal to 3

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0since I had something square and i took the square root of it that made me think of the absolute value thing where you change the sign of the number when the inequality sign is flipped

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ohh, ok that's right, i think i understand now, that was the one part that i didn't follow

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you so much for your help!

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0the first time i did part one i got the interval wrong i don't know if you notice i corrected myself on that one or not

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, i saw, thank you for checking

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0we know that interval is true since the question said if it was true right?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0so we based everything off that result

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0exactly, i think we have to assume that base on the problem

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0yes we do because the question says too

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i really like that problem that was totally awesome goodnight!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks so much for your help, good night to you too!
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