SOLUTION: {{{ (2/3)x^2-3x+6=y }}} I need to find the vertex and axis of symmetry to graph the quadratic form, I understand how to graph quadratic forms but the fraction in this specific pro

Question 341749: I need to find the vertex and axis of symmetry to graph the quadratic form, I understand how to graph quadratic forms but the fraction in this specific problem has me all jumbled up. I tried solving it and got x= 9/4 for the axis of symmetry and (9/4,87/16)for the vertex but im almost 100% certain that is wrong. I would really appreciate some help (PLEASE HELP ME). Thanks in advance.
-Kay
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find the vertex and axis of symmetry, we need to complete the square for

Start with the given expression.

Factor out the coefficient . This step is very important: the coefficient must be equal to 1.

Take half of the coefficient to get . In other words, .

Now square to get . In other words,

Now add and subtract inside the parenthesis. Make sure to place this after the "x" term. Notice how . So the expression is not changed.

Group the first three terms.

Factor to get .

Combine like terms.

Distribute.

Multiply.

So after completing the square, transforms to . So .

So is equivalent to .

So the equation is now in vertex form where , , and

Remember, the vertex of is (h,k).

So the vertex of is since and

Also, remember that the axis of symmetry is simply . So the axis of symmetry is

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
I need to find the vertex and axis of symmetry to graph the quadratic form, I understand how to graph quadratic forms but the fraction in this specific problem has me all jumbled up. I tried solving it and got x= 9/4 for the axis of symmetry and (9/4,87/16)for the vertex but im almost 100% certain that is wrong. I would really appreciate some help (PLEASE HELP ME). Thanks in advance.
------------------------
axis of symmetry is x = -b/2a
x = 3/(4/3) = 9/4
-------------------
The vertex is (9/4,f(9/4))
f(9/4) = (2/3)*(81/16) - 27/4 + 6 = 27/8 - 27/4 + 6 = -27/8 + 6 = 21/8
--> (9/4,21/8)
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