Question

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

Answer 1

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?

Answer 2

need help getting 2 values of x ??

Answer 3

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

Answer 4

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

x^2 + x - 6= 0

Answer 5

Oh yeah you subtract not add

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

they aren't gonna be whole numbers?

Answer 10

one of the number is negative

Answer 11

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

Answer 12

This is so simple why isn't it clicking?

Answer 13

oh my god i'm an idiot

Answer 14

okay so it's -2 and 3

Answer 15

yes!

Answer 16

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

Answer 17

x^2 + x - 6= 0

factorization method

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

Answer 18

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

Answer 19

x(x+3) - 2 (x+3) = 0

want to continue?

Answer 20

sorry how did you get there again?

Answer 21

from x^2 +3x ,
i factored out x

so i got
x(x+3)

Answer 22

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

Answer 23

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

Answer 24

the +3x??

i splitted +x into 3x -2x

Answer 25

ohhhh!!

Answer 26

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

Answer 27

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 ??

Answer 28

.... 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

Answer 29

okay i've got that now

Answer 30

so,
x = -3 or x = 2


now you can plug these values in x+y = 9 :)

Answer 31

oh okay okay and that will be 12 and 7?

Answer 32

yes

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

Answer 33

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

Answer 34

i meant 2 yeah
okay yay that's it?

Answer 35

yes, thats it :)

Answer 36

thank you so much sorry for being so slow lol

Answer 37

welcome ^_^
and no problem