Question 1106825: I am trying to figure out how to do this problem, but I am dyslexic and can't do it on my own. Can you help?
f(x)=x^2+2
in the book, our goal is to find the domain of these functions.
Take your time.
-Thanks
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! Use the form ax^2+bx+c, to find the values of a, b, and c:
a=1,b=0,c=2 (the problem tells you this)
Now the vertex form of a parabola:
a(x+d)^(2)+e
Find the value of d:
d= b/2a; d = 0/2*1; d = 0
Find the value of e:
e = c-(b^2/4a; e = 2-(0^2/(4*1); e = 2-0/4 = 2
The vertex form:
a(x+d)^(2)+e In order to plot this we need an equation (we need two mathematical expressions that are equal = ):
y = a(x+d)^(2)+e Since the value of a is 1 (we only have 1 x) we can rewrite:
y = (x+d)^(2)+e
Let's plug in the values I just calculated into this equation:
y = (x+0)^(2)+2
There are some other values we need to find, these are easy because I just did all the work:
In the vertex form y = a(x-h)^(2)+k find the value of a, h, and k
a = 1
h = 0
k = 2
Since the value of a is positive, our parabola opens up
The vertex (h, k) is (0, 2), so this is where the parabola starts, and goes up to infinity. We write this as
[2, ∞)
{y|y≥2}
Domain: (−∞,∞),{x|x∈R} for any integer n
range: [2,∞),{y|y≥2}
Graph:
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