A rectangle has vertices at (0, 0), (3, 0), and (0,6). What is the area of the rectangle?
1 answer:
You might be interested in
Answer: Choice B) (2,0)
======================================
Set the first piece equal to zero and solve for x
x^2 - 4 = 0
x^2 = 4
x = sqrt(4) or x = -sqrt(4)
x = 2 or x = -2
Keep in mind that the first piece y = x^2-4 is only graphed when x = 2 or larger, so we ignore x = -2. This is one x intercept, but there may be more. Let's check the other graph to see what we get.
----------
Set the second piece equal to zero and solve for x
x-2 = 0
x-2+2 = 0+2
x = 2
We get the same result as above in the prior section. Because of this, the two pieces connect at this junction point.
The x intercept x = 2 leads to the location (2,0). The x intercept always occurs when y = 0.
The graph below shows this.
side note: the red piece y = x^2 - 4 looks linear, but it's actually not a straight line. It's just a really stretched out curve.
