OpenStudy (anonymous):

What are the intersection points of the equations p(x,y)=(t,t^2 + 3) and x+y=9? Best explanation gets medal!

1 year ago
hartnn (hartnn):

Lets first make an equation in x and y from the parameterized equation in t. x,y = t, t^2 +3 x= t, y = t^2+3 so, y= x^2 + 3 now solve this simultaneously with x+y = 9 plug in y = x^2+3 here x + x^2 + 3 = 9 this is a simple quadratic in x which will give you 2 roots :) can you get those?

1 year ago
hartnn (hartnn):

need help getting 2 values of x ??

1 year ago
OpenStudy (anonymous):

It would turn into t^2 + t + 12 = 0 right?

1 year ago
hartnn (hartnn):

12? we subtract 9 from both sides, x^2 +x + 3 - 9 = 0 x^2 + x - 6= 0

1 year ago
OpenStudy (anonymous):

Oh yeah you subtract not add

1 year ago
OpenStudy (anonymous):

I'm just confused because it needs to multiply to equal 1 but adds up to -6

1 year ago
hartnn (hartnn):

2 numbers which multiply to -6 and adds upto +1

1 year ago
OpenStudy (anonymous):

sorry that's what i meant can't be 3 & 3 or 6 and 1

1 year ago
OpenStudy (anonymous):

they aren't gonna be whole numbers?

1 year ago
hartnn (hartnn):

one of the number is negative

1 year ago
OpenStudy (anonymous):

Ugh sorry I've been out sick from school for two weeks lol

1 year ago
OpenStudy (anonymous):

This is so simple why isn't it clicking?

1 year ago
OpenStudy (anonymous):

oh my god i'm an idiot

1 year ago
OpenStudy (anonymous):

okay so it's -2 and 3

1 year ago
hartnn (hartnn):

yes!

1 year ago
OpenStudy (anonymous):

okay wow that was quite a journey, so now that i have that, i need to find numerical values right?

1 year ago
hartnn (hartnn):

x^2 + x - 6= 0 factorization method z^2 + 3x - 2x - 6= 0

1 year ago
hartnn (hartnn):

x^2 + 3x - 2x - 6= 0 ***

1 year ago
hartnn (hartnn):

x(x+3) - 2 (x+3) = 0 want to continue?

1 year ago
OpenStudy (anonymous):

sorry how did you get there again?

1 year ago
hartnn (hartnn):

from x^2 +3x , i factored out x so i got x(x+3)

1 year ago
OpenStudy (anonymous):

and where did the x+3 come from? one of the possible t values i factored out?

1 year ago
OpenStudy (anonymous):

oh you just factored it out and then that is part of it

1 year ago
hartnn (hartnn):

the +3x?? i splitted +x into 3x -2x

1 year ago
OpenStudy (anonymous):

ohhhh!!

1 year ago
OpenStudy (anonymous):

what happens now with x(x+3) ??

1 year ago
OpenStudy (anonymous):

wait, can't I just plug in the x values into the x+y=9 equation as an x= ? like -2 = -y + 9 and 3 = -y + 9 ??

1 year ago
hartnn (hartnn):

.... because we still don't have the values of x! so we are here x(x+3) - 2 (x+3) = 0 factor out x+3 (x+3)(x-2) = 0

1 year ago
OpenStudy (anonymous):

okay i've got that now

1 year ago
hartnn (hartnn):

so, x = -3 or x = 2 now you can plug these values in x+y = 9 :)

1 year ago
OpenStudy (anonymous):

oh okay okay and that will be 12 and 7?

1 year ago
hartnn (hartnn):

yes so your solutions are -3,12 and 2,7

1 year ago
OpenStudy (anonymous):

(-3,12) AND (7,7) ?

1 year ago
OpenStudy (anonymous):

i meant 2 yeah okay yay that's it?

1 year ago
hartnn (hartnn):

yes, thats it :)

1 year ago
OpenStudy (anonymous):

thank you so much sorry for being so slow lol

1 year ago
hartnn (hartnn):

welcome ^_^ and no problem

1 year ago