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Question 481534: I'm struggling with this. I need to find the vertex, line of symmetry, and the max or min value of f(x).
The equation is f(x)=1/3 (x+7)^2 + 9
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f(x) = (1/3) * (x+7)^2 + 9
multiply it out to get:
f(x) = (1/3) * (x^2 + 14x + 49) + 9
this becomes:
(1/3)x^2 + (14/3)x + (49/3) + 9 which becomes:
(1/3)x^2 + (14/3)x + (49/3) + (27/3) which becomes:
(1/3)x^2 + (14/3)x + (76/3)
this is a quadratic equation in the form of ax^2 + bx + c
a = (1/3)
b = (14/3)
c = (76/3)
the x value of the vertex is given by the equation x = -b/2a.
that would be (-14/3)/(2/3) which is equal to (-14/3) * (3/2) which is equal to (-7).
the y value of the vertex would be f(-7) which would be equal to:
(1/3)(49) + (14/3)(-7) + (76/3) which becomes:
(49/3) - (98/3) + (76/3) which becomes:
27/3.
the coordinates of the vertex of the equation becomes (x,y) = (-7,27/3).
that's also the max/min point.
the axis of symmetry of the graph is at x = -7.
a graph of your equation looks like this:
that vertical line is at x = -7.
that horizontal line is at y = (27/3).
that vertical line is the axis of symmetry.
the intersection of the vertical line and the horizontal line is the vertex of the graph.
it is also the max/min point of the graph.
Answer by ikleyn(52866)  (Show Source):
You can put this solution on YOUR website! .
I'm struggling with this. I need to find the vertex, line of symmetry, and the max or min value of f(x).
The equation is f(x)=1/3 (x+7)^2 + 9
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In his post, tutor @Theo makes a lot of unnecessary calculations.
If you will follow his solution, your teacher will see that you do not understand the basic conceptions
of the subject.
The problem can be and should be solved in couple of lines.
Do not follow the @Theo' solution, since it is wrong way teaching.
You are given an equation of a parabola in the vertex form.
Having this equation, you immediately see that the line of symmetry is x=-7
and the vertex point is (-7,9).
Minimum value of the function is 9 at x = -7 (at the vertex point).
Solved.
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This is all that your teacher wants to get from you.
I don't know, for what reason tutor @Theo to bulk up tons of unnecessary calculations in many
of his posts. It is definitely wrong style teaching --- I would even say - unacceptable style of teaching.
It is why I re-write one his "solution" after another.
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