Which of the following expressions are perfect-square trinomials? Check all of the boxes that apply.
2 answers:
Perfect squares follow this pattern:
So, two terms must be perfect squares of two certain roots. If so, the remaining term must be twice their product. Let's analyse the trinomials one by one:
1) x^2 is the square of x. -64 is not a perfect square. So, the trinomial is not a perfect square.
2) 4x^2 is the square of 2x. 9 is the square of 3. The remaining term, 12x, is indeed twice their product. So, we have
3) x^2 is the square of x. 100 is the square of 10. The remaining term, 20x, is indeed twice their product. So, we have
4) x^2 is the square of x. 16 is the square of 4. The remaining term, 4x, is not twice their product (it's only the product of 4 and x, so it should be doubled). So, this trinomial is not a perfect square.
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Answer:
We have the function:
f(x) = x^3 - 2*x^2
To sketch this, we need to graph some points, and then just draw a line that passes through the points.
The graph of this equation is shown below.
Now we can complete the question.
If the graph is below the x-axis in some interval, the function is negative in that interval
If the graph is above the x-axis in some interval, the function is positive in that interval.
If the graph goes up in a interval, then the function is increasing in that interval
If the graph goes down on an interval, then the function is decreasing in that interval.
Then:
1) f is------ on the intervals (−∞, 0) and (0, 2).
Here we can see that the graph is below the x-axis in those intervals, then here we have:
f is negative on the intervals (−∞, 0) and (0, 2).
2) f is------ on the interval (2,∞)
Here the answer is positive:
f is positive on the interval (2,∞)
3) fi is ------ on the interval (0, 4/3)
In the graph, you can see that the graph goes down in that interval, then the correct answer here is:
f is decreasing on the interval (0, 4/3)
4) f is------ on the intervals (−∞, 0) and (4/3, ∞).
In this case, we can see that the graph goes up in these intervals, then the correct answer here is:
f is increasing on the intervals (−∞, 0) and (4/3, ∞).
