T or F: The graph of y = | 2x^2 + 4 | never touches the x axis.?

Question

^ is an exponent

Answer 1

y = |2x^2 + 4|
y = |2(x^2 + 2)|

since x^2 + 2 can't be factored, this problem never touches the x-axis

TRUE

Answer 2

True... the closest will be when x=0 and y=4. You can prove this as well by noticing that the absolute value will always result in a positive number or 0 (zero). Therefore, to touch the x-axis it would have to do so at 0 (zero). Setting 2x^2+4=0 and solving for x results in x = Sqrt (-2) so unless you are plotting imaginaray numbers (in this case ~1.414i) then y will never equal zero or less than zero and therefore never touch the x-axis.

Answer 3

The graph of the function would be the same with or without the "absolute value" notation. In either case, the closest it gets to the x-axis is at (0, 4).

Answer 4

True.
Because y is not equal to zero for any x, as shown below:

y
= | 2x^2 + 4 |
>= 2x^2 + 4
>= 4

Answer 5

true...
In addition to the calculations given by others, you can make a simple t chart to graph the equation. I believe that most students nowadays have neat calculators that will graph as well. Anyway, the graph starts at (0,4) and goes upward, hence never touching the x-axis.

Answer 6

The truth value of that statement depends on the domain you are restricting x to. I assume you are dealing with only real numbers so the answer is True.

Answer 7

True, "y" will never be less than 4

Answer 8

True, this function it is always a positive function.

Answer 9

maybe you should get a tutor instead of trying to get free answers for your homeowrk

Answer 10

true