IanStewart wrote:
GMATBaumgartner wrote:
The line represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1
A. y = 2x^2+5x+1
...
I'd emphasize that none of the equations in this question represent
lines, despite what the question appears to say. The equations represent parabolas, and you don't need to know about parabolas for the GMAT.
There is one concept in this question that is occasionally tested - the concept of translation. If you have any equation at all in coordinate geometry, say:
y = x^2
that will be some curve in the coordinate plane (technically it will be a 'parabola', or U-shape). If you then modify the equation by adding a constant on the right side, say by adding 5:
y = x^2 + 5
then the graph of this new equation will look exactly the same as the graph of the first equation, except that it will be exactly 5 units higher. So when we add a constant on the right side of an equation, we're simply moving the picture of the equation up or down.
I think Bunuel and Ian have provided sufficient information to solve this problem.
Lines are always represented by LINEAR equations (equations that have maximum degree of the variables as 1). A quadratic equation (max. degree =2) can NEVER represent lines.
I would like to add one thing that people who are not familiar with 'conics', usually do not remember that \(y^2=4ax\) is the standard equation of a parabola. One way to eliminate such rote learning is to look at an equation and plot 2-3 points and see what shape of the curve do you get and then proceed from there. GMAT does not require you to remember fancy names.
\(y^2=4ax\) and \(y^2=4ax+Z\), where Z is any value (4,5,7.8,0.4 etc). These curves belong to 'same family' of parabolas with the only exception that these 2 curves will have their vertices offset by 'Z' amount.
Finally, for the curious minds out there, the attached picture shows all the possible combinations of 'simple' parabolas.
Attachments
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