The function, f(x) = |x - 2| + 4 has a vertex that is located in which quadrant?
2 answers:
Answer: Quadrant I
Step-by-step explanation:
The standard equation of the absolute function is given by:
, where
is the vertex of the absolute function.
The given absolute function :
Comparing to the standard absolute function, the vertex of the given absolute function = (2,4)
Since both the coordinates of the vertex is positive, therefore the vertex lies in Quadrant I .
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Answer:
Step-by-step explanation:
The identities you need here are:
and
You also need to know that
x = rcosθ and
y = rsinθ
to get this done.
We have
r = 6 sin θ
Let's first multiply both sides by r (you'll always begin these this way; you'll see why in a second):
r² = 6r sin θ
Now let's replace r² with what it's equal to:
x² + y² = 6r sin θ
Now let's replace r sin θ with what it's equal to:
x² + y² = 6y
That looks like the beginnings of a circle. Let's get everything on one side because I have a feeling we will be completing the square on this:
Complete the square on the y-terms by taking half its linear term, squaring it and adding it to both sides.
The y linear term is 6. Half of 6 is 3, and 3 squared is 9, so we add 9 in on both sides:
In the process of completing the square, we created within that set of parenthesis a perfect square binomial:
And there's your circle! Third choice down is the one you want.
Fun, huh?
Answer:
A)
B)
Step-by-step explanation: