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Points at which graph intersects x-axis

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by gmattesttaker2 » Tue May 20, 2014 5:23 pm
Hello,

Can you please assist with this:

The figure shows the graph of y = (x+1)(x-1)^2 in the xy-plane. At how many points does the graph of y = (x+1)(x-1)^2 + 2 intersect the x-axis?

A) None
B) One
C) Two
D) Three
E) Four

OA: One


Thanks a lot,
Sri
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by [email protected] » Tue May 20, 2014 5:45 pm
Hi Sri,

As complex as this question appears, it's actually based on a simple graphing rule (and a bit of "cause and effect").

When a graphing equation is written in "slope-intercept" format (meaning Y = something), you "plug in" a number for X and get a resulting number for Y. Then you graph each co-ordinate.

In this question, notice that the only difference between the two equations is the "+2" that's added to the end. So, by plugging in a value of X into the original equation, you get a value for Y. NOW when you plug in a value of X, you get a result that is +2 BIGGER. The graph will look exactly the same, but it will "shift" 2 spots "up" the XY plane (because the value of Y has increased by 2).

In the original graph, there are 2 points that hit the X-axis. By shifting the entire graph "up" 2 spots, there will be just ONE.

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