Question 132221: Find the vertex, the line of symmetry, and the maximum/minimum value of f(x). Then, graph the function.
f(x) = -(x+2)^2 - 4
The vertex is:
The line of symmetry is:
The maximum/minimum value is:
Graph the function.
Answer by nycsharkman(136)   (Show Source):
You can put this solution on YOUR website! Your question:
Find the vertex, the line of symmetry, and the maximum/minimum value of f(x). Then, graph the function.
f(x) = -(x+2)^2 - 4
The vertex is:
The line of symmetry is:
The maximum/minimum value is:
Graph the function.
You have parabola here in the form y = a(x - h)^2 + k.
First of all, y = f(x) and vice-versa. These two symbols are interchageable.
In other words, f(x) = -(x + 2)^2 - 4 can also be written using the letter y
like this y = -(x + 2)^2 - 4. They're both the same thing.
Secondly, do you see the letter [a] in the general form y = a(x - h)^2 + k?
If the letter a is NEGATIVE (and it is negative for your question), the graph of this parabola will open downward. This means the maximum point of the graph will be ON TOP (like looking at a hill).
Let's go back to your question.
The vertex of the parabola is in the form of a point called (h, k).
The vertex point (h, k) determines the MAX or MIN of the parabola.
Your vertex is the point (-2, 4). Where did I get these numbers?
Do you see the number +2 and -4 in your question?
The number +2 represents h and -4 represents k in the general form given above. To find the vertex, simply change the signs in front of h and k to the OPPOSITE value and you will find the vertex of the parabola.
The maximum value is the vertex. So, the maximum value is the point (-2, 4).
There is no minimum value for this function because the parabola faces downward.
You said line of symmetry, right? I am sure that you meant to type axis of symmetry.
What is the axis of symmetry? The axis of symmetry is the line that CUTS the parabola exactly in two equals parts at the vertex. It is line that goes through the vertex dividing the parabola into two EQUAL pictures.
The axis of symmetry is the equation x = h.
Do you know the value of h? You sure do. We want it above, right?
The axis of symmetry is the value of h as given in the vertex point or simply x = -2. That is your axis of symmetry.
To graph the parabola, visit this link for detail:
http://www.purplemath.com/modules/grphquad.htm
I hope this helps.
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