Question 625231: f(x)=1/2(x+9)^2+7
I got 95/2 but I am confused because I have never run into a problem with no x-intercept. So how do I write an ordered pair for the vertex?
Found 2 solutions by KMST, Alan3354:
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website!  is a quadratic function.
As such, its graph is a parabola.
Unlike linear functions, which graph as straight lines, quadratic functions are allowed to have no x-intercept.
They may approach the x-axis for a while, but then they change their mind and turn away from the x-axis, never crossing it.
For your function:
 for 
For any other value of x,
 and 
There is no x-intercept, because  for all values of x.
The graph never crosses the x-axis (the y=0 line), because  is never zero.
The function has a minimum at with 
The vertex of the parabola is at that point: point(-9,7).
Your function graphs as this:
Quadratic functions can be written in the form
 or 
with  ,  , and  being some real numbers (and a must not be zero).
When written in that form, (h,k) is the vertex, and tells you how curvy the curve is and which way it goes.
The larger the absolute value of , the curvier the curve is.
If is positive, the curve goes up from the vertex on both sides, as  gets larger and larger. It looks like a smiley mouth.
If is negative, the curve goes down from the vertex on both sides, as gets larger and larger. It's frowning.
Your curve is smiling at you.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! f(x)=1/2(x+9)^2+7
I got 95/2 but I am confused because I have never run into a problem with no x-intercept. So how do I write an ordered pair for the vertex?
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The vertex is (-9,7)
95/2 for what?
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