Solving two equations

Question

 and need to find where they intersect.

y = x - 1 and the parabola

y^2  = 2x + 6

I know I set them equal to each other.  But every time I solve it I get one point wrong.

One time I'll find (-1,-2) and another time I try I will get (5,4) but every time I only get one of these and get the other one wrong, I can't solve and get both correct answers together.

Answer 1

y = x - 1 and the parabola
y^2  = 2x + 6

 

x=y+1

x=(y²-6)/2 equating the two expressions for x

2y+2=y²-6

y²-2y-8=0

(y-4)(y+2)=0

y=4, y=-2

substituting in the first equation 4=x-1  x=5   (5,4)

-2=x-1   x=-1   (-1,-2)

Answer 2

HI Robb:

 

Substituting, we get (x - 1)² -2x - 6 = 0.

 

That is X² - 2x + 1 - 2x - 6 = 0,

 

that is x² - 4x - 5 = 0,

 

that is (x- 5)(x + 1) = 0.

 

The TWO roots of this quadratic are x = 5 and x = -1.  This gives y = 4 when x = 5 and y = -2 when x = -1.

 

So the points where the two curves intersect at (5, 4) and (-1, -2).

 

Draw a graph and check.

 

Dattaprabhakar (Dr. G.)