what are the points of intersection for x*2 + 5x + 6=y and y=2x-6.?

Question

i haveta find the intersections but i believe that there are none in this equation. any ideas what happens after x*2+3x+14= ??
any help is much appreciated :)

Answer 1

You would set your two equations equal to each other to solve:

y = 2x-6
y = x² + 5x + 6

So, 2x-6 = x² + 5x + 6

Subtract 2x from both sides:

-6 = x² + 3x + 6

Add 6 to both sides:

0 = x² + 3x + 12

Now you can factor or use quadratic formula to solve for x. (I don't see any way that this can be factored, unfortunately, so we'll have to use the ol' quadratic formula.)

x = [ -3 ± √ (3*3 - 4*1*12) ] ÷ 2*1 =

[ -3 ± √ (-39) ] ÷ 2

This equation has complex roots, but no real roots. Therefore in your real plane these two graphs do not intersect.

.

Answer 2

2 things equal to y are equal to each other.
x² + 5x + 6 = 2x - 6
x² + 3x + 12 = 0 .......(where'd you get +14?)
y = x² + 3x + 12 opens up, has a vertex at (-1.5, 9.75), and doesn't cross the x axis, so it has no real solutions. That means there are no points of intersection.

A good precalc question would be, "how close does the line get to the parabola?" Or maybe that one requires calculus.

Answer 3

x^2 + 5x + 6 = 2x - 6
x^2 + 3x + 12 = 0

(-3 +/- sqrt(9 - 48))/2

You got yourself some imaginary numbers there... in other words, those two equations do not intersect.

Answer 4

x*2 + 5x + 6=y and y=2x-6
2x - 6 + 5x + 6 = 2y