Question

A curve with equation y = x^2 + 2x + 3 crosses a straight line with equation y = x+9 in two places. Find the coordinates of the two points where the lines intersect.

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Answer 1

Got you fam or whatever people say....


We have equation 1 and 2
1.
`y= x^(2) +2x+3`
2.
`y=x+9`

Because equation 2 is simple and isn't quadtratic, we will insert 2 into 1,


`x+9= x^(2) +2x+3`

`0= x^(2) +x-6`

Then factor
x² +x -6=0
(x+3)(x-2)=0
x= -3, 2

Then using the values of x insert into either equation 1 or 2 to find y. I'm doing 2 because I'm lazy

y= x+9

when x=-3
y=x+9
= -3+9
= 6

(-3,6)

when x =2
y=x+9
= 2+9
= 11

(2,11)

Hence the co-ordinates are (2,11) and (-3,6)