SOLUTION: Plot each pair of equations, then what is their intersection points? y1=x^2-1 Y2=-1 I did x^2-1=-1 = x^2-1=1=0 = x^2=0 = x=0 But I don't know how to plot them.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Plot each pair of equations, then what is their intersection points? y1=x^2-1 Y2=-1 I did x^2-1=-1 = x^2-1=1=0 = x^2=0 = x=0 But I don't know how to plot them.       Log On


   

Question 82935: Plot each pair of equations, then what is their intersection points?
y1=x^2-1
Y2=-1
I did
x^2-1=-1
= x^2-1=1=0
= x^2=0
= x=0
But I don't know how to plot them.
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
I did
x^2-1=-1 <=== Good. You did this by setting Y1 equal to Y2
.
x^2-1=1=0 <=== A little confusing here. What you need to do is to get the x^2 term by itself
on the left side. To do that you eliminate the -1 on the left side by adding +1 to both sides.
When you do that you get the next equation that you got.
.
x^2=0 <=== This is correct.
.
x=0 <=== This is also correct. It tells you that when x equals zero, the two equations
you originally were given have equal values of y. Return to the original equations
and substitute zero for x and you get:
.
Y1 = x^2 - 1
.
Then substituting zero for x results in:
.
Y1 = 0 -1 = -1
.
The second equation that you were given was:
.
Y2 = -1
.
Since this equation does not contain an x term, Y2 is -1 no matter what value is assigned
to x.
.
From the first equation you know that (0, -1) is the point that has a Y value of -1. And
from the second equation you know that (0, -1) is also a point that is common with the
solution of the first equation.
.
What this all means is that (0, -1) is the point that these two equations have in common.
And what is going on is that the graph of the first equation is a parabola that as you move
to the right drops down to its minimum value of -1 [at the point (0, -1)] and then as
you continue to move to the right rises. The Y axis is the line about which this parabola
is symmetrically centered.
.
In the meantime the line Y2 = -1 is a horizontal line that is tangent to the bottom of
the parabola of the first equation at the point (0, -1). So there is only one point of
intersection ... and that is the point (0, -1). The coordinate system below shows the
graphs you should have:
.
graph%28300%2C300%2C+-10%2C10%2C-10%2C10%2C+x%5E2-1%2C-1%29
.
Hope this helps to clarify the points you were looking for.
.