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Home Q & A Board Science-Related Homework Help Mathematics
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lensley lensley
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11 years ago
Like if I had an equation of a parabola and the equation of a line, how do I tell if they intersect? Without graphing of course.
For example:
y= -2(x+2)(x-4)
and
y=-1

Thank you so much for everyone's help. I appreciate it a lot.
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wrote...
#1
11 years ago
The intersect is when both y and x are the same.
So set the above equation to -1 and see what x is.
wrote...
#2
11 years ago
Try finding when the parabola reaches y = -1
So plug in -1 for y and solve for x
-1= -2(x+2)(x-4)
1/2 = (x+2)(x-4)
x^2 -2x - 8 = 1/2
x^2 - 2x - 8.5 = 0

So yeah it intersects ...u know this when u use a quadratic formula
wrote...
#3
11 years ago
Convert it to a single equation and use the quadratic formula or other method to solve.

Step 1.  Set the first equation equal to the second.  They intersect if they have the same y coordinate and the same x coordinate at any point.  So

-2(x+2)(x-4) = -1

Step 2.  Put this in a form you are familiar with:

-> -2(x^2 -2x - 8) = -1
-> -2x^2 + 4x + 17 = 0

If there is a solution than the two intersect.  If there is no solution they do not intersect.
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