How many times will the graph of y = –x intersect the graph of y = x2 – 3 ?

Question

parthkohli · Answer

Actually, you can equate $-x$ and $x^2 - 3$

lgbasallote · Answer

equate them to one another
$$x^2 - 3 = x$$
now solve for x
$$x^2 + x - 3 = 0$$
now use the discriminant to find out how many positive roots are there
$$b^2 - 4ac = 1^2 - 4(1)(-3) \implies 1 + 12 \implies 13$$
it's positive therefore there are two roots. therefore it crosses twice

lgbasallote · Answer

got it?

parthkohli · Answer

Since the solution sets will be the same, the point will be the same.. and so we'd have an intersection of those functions.

parthkohli · Answer

Why $x^2  - 3 = x$? Why not $x^2 - 3 = -x$?

lgbasallote · Answer

uhh typo @_@

lgbasallote · Answer

$$x^2 - 3 = -x$$
solve for x
$$x^2 + x - 3 = 0$$
now use discriminant to find how many roots are there
$$b^2 - 4ac \implies (1)^2 - 4(-3)(1) \implies 1 + 12 \implies 13$$
positive so there are 2 roots therefore crosses twice

rayford · Answer

thanks alot! u shold be a teacher man!

lgbasallote · Answer

i am haha

rayford · Answer

oh....well

rayford · Answer

you are good!