Parabola: convert y=-3/8(x-4)^2+6 to standard form

helpsalot

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Nov 24, 2016
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Thanks for your help, in the end I just graphed the parabola and was able to find the equation in factored form quiet easily. I would like a second opinion on a different question now though.
I had to convert
y=-3/8(x-4)^2+6
to standard form and got
y=3/8x^2+4x
does this look right to you.
 
Typo

Sorry there was a typo in that last post. The equation I actually got was
y=-3/8x^2+3x
Thanks
 
Thanks for your help, in the end I just graphed the parabola and was able to find the equation in factored form quiet easily. I would like a second opinion on a different question now though.
I had to convert
y=-3/8(x-4)^2+6
to standard form and got
y=3/8x^2+4x
does this look right to you.
It is impossible to make out what you are saying. Is all of 8(x-4)^2+6 in the denominator? Is just the 8 in the denominator and (x-4)^2+6 in the top??

The way you wrote it is \(\displaystyle y=\dfrac{3}{8(x-4)^2}+6\). You can write this as y= 3/(8(x-4)^2) + 6

Do you mean \(\displaystyle y=\dfrac{3}{8}\ (x-4)^2+6 ?\) You can write this as (3/8)((x-4)^2)+6

Or maybe \(\displaystyle y=\dfrac{3}{8}\ ((x-4)^2+6) ?\) You can write this as (3/8)((x-4)^2+6)

Or \(\displaystyle y=\dfrac{3}{8(x-4)^2+6}?\) You can write this as 3/(8(x-4)^2+6)
 
Last edited:
Thanks for your help, in the end I just graphed the parabola and was able to find the equation in factored form quiet easily. I would like a second opinion on a different question now though.
I had to convert
y=-3/8(x-4)^2+6
to standard form and got
y=3/8x^2+4x
does this look right to you.
As Jomo said that is very ambiguous. I think the most reasonable interpretation is y= -(3/8)(x- 4)^2+ 6. Multiplying out that square, y= -(3/8)(x^2- 8x+ 16)+ 6= -(3/8)x^2+ 3x- 6+ 6= -(3/8)x^2+ 3x.

So what you have in your second post is correct.
 
I think you need to tell us what YOU understand the "standard form for the equation of a parabola" to be.....

I have seen it defined this way:

y = ax2 + bx + c


What you consider as standard form will give you direction in how to approach the problem.
 
It is impossible to make out what you are saying.

No, it is not impossible. Just follow the Order of Operations. :)


The way you wrote it is \(\displaystyle y=\dfrac{3}{8(x-4)^2}+6\).

No, that is not the meaning.

The Order of Operations tells us (in part) to do multiplication and division as they occur, working from left to right.
 
As Jomo said that is very ambiguous.

I do not agree that the posted expression is very ambiguous. It seems clear enough to me, from context, that the independent variable is not in the denominator of a ratio.

(At least you answered the poster's question.)
 
I think you need to tell us what YOU understand the "standard form for the equation of a parabola" to be.

Mrspi makes a good point. At the college where I work, different instructors use different definitions for the standard form of a quadratic equation. I have also seen three different definitions presented in text books, over the years.

y = ax^2 + bx + c could be standard form or general form, depending on the instruction.

y = a(x - h)^2 + k could be standard form or vertex form, depending on the instruction.

0 = ax^2 + bx + c could be standard form or general form, depending on the instruction.

I would not be surprised to see other definitions, names, or forms, as math education is far from consistent.
 
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