SOLUTION: which of the following is not in range of f(x)= 7(x-2)^2 A. 300 B. 6 c. -3 D. 12 So my first idea was to plug in each number and then I realized that didn't help. I'm not real

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Question 884127: which of the following is not in range of f(x)= 7(x-2)^2
A. 300
B. 6
c. -3
D. 12
So my first idea was to plug in each number and then I realized that didn't help. I'm not really sure how to even start on this problem
Found 2 solutions by jim_thompson5910, Theo:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
x^2 is NEVER negative. Squaring a positive number leads to a positive number. Squaring a negative number gives you a positive result (eg: x = -3 ---> x^2 = (-3)^2 = 9)

So that means (x-2)^2 is NEVER negative based on the same reasoning as above.

Multiplying some number that's either 0 or positive by 7, which is positive, means the expression 7(x-2)^2 results in a number that's 0 or some positive number.

7(x-2)^2 is NEVER negative.

Therefore, c) -3 is NOT a possible output of the function. It's impossible to generate a negative number.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
one way is to graph it.
that should tell you what value is not possible.

the other way is to use logic or just solve the equation for each of the values indicated to see which value is not possible.

if the value is possible it is within the range.

if the value is not possible it is not within the range.

you can also see right off that bat that (x-2)^2 has to be positive.

it can't be negative because (-x)^2 = (-x) * (-x) = x^2

that points to -3 as not being possible.

let's see if we can prove that by solving the equation for f(x) = -3

we get 7(x-2)^2 = -3
divide both sides of this equation by 7 to get:
(x-2)^2 = -3/7
take the square root of both sides of this equation to get:
x-2 = +/- sqrt(-3/7)
since you cannot take the square root of a negative number and get a real number answer, then selection c is the one that is not possible.

the graph of this equation looks like this:

looking at the graph you can see that it never gets below 0.

the range is all values of x >= 0.