Answer:
S' (-6, 6)
T' (2, 6)
U' (2, 0)
V' (-6, 0)
Step-by-step explanation:
To reflect the rectangle over the x-axis, think of it as flipping it over the x-axis. On the graph, count the units from V to S, it's 6 units. So, from the x-axis, count 6 units up from V. S would lie on -6, 6. Do the same for W to T. T would lie on (2, 6). The remaining coordinates U and V don't change because it is <em>already </em>on the x-axis. <em> </em>
The correct answer is C.
You can tell this by factoring the equation to get the zeros. To start, pull out the greatest common factor.
f(x) = x^4 + x^3 - 2x^2
Since each term has at least x^2, we can factor it out.
f(x) = x^2(x^2 + x - 2)
Now we can factor the inside by looking for factors of the constant, which is 2, that add up to the coefficient of x. 2 and -1 both add up to 1 and multiply to -2. So, we place these two numbers in parenthesis with an x.
f(x) = x^2(x + 2)(x - 1)
Now we can also separate the x^2 into 2 x's.
f(x) = (x)(x)(x + 2)(x - 1)
To find the zeros, we need to set them all equal to 0
x = 0
x = 0
x + 2 = 0
x = -2
x - 1 = 0
x = 1
Since there are two 0's, we know the graph just touches there. Since there are 1 of the other two numbers, we know that it crosses there.
