# Thread: Issue with Converting to Standard Form

1. ## Issue with Converting to Standard Form

I have this problem. Convert to standard form.

-2x2-6x+10

The answer I come up with does not work when I check my work. What did I do wrong?
-2(x+1.5)2+14.5

C-
x

2. ## Re: Issue with Converting to Standard Form

It's hard to point out where you went wrong when we don't know what you actually did to get that answer...

\displaystyle \begin{align*} -2 \, x^2 - 6 \, x + 10 &= -2 \, \left( x^2 + 3 \, x - 5 \right) \\ &= -2 \, \left[ x^2 + 3\,x + \left( \frac{3}{2} \right) ^2 - \left( \frac{3}{2} \right) ^2 - 5 \right] \\ &= -2 \, \left[ \left( x + \frac{3}{2} \right) ^2 - \frac{9}{4} - \frac{20}{4} \right] \\ &= -2 \, \left[ \left( x + \frac{3}{2} \right) ^2 - \frac{29}{4} \right] \\ &= -2 \, \left( x + \frac{3}{2} \right) ^2 + \frac{29}{2} \end{align*}

3. ## Re: Issue with Converting to Standard Form

Originally Posted by jennasam400
I have this problem. Convert to standard form.

-2x2-6x+10

The answer I come up with does not work when I check my work. What did I do wrong?
-2(x+1.5)2+14.5

C-
x

on expanding the answer you get

$-2(x+1.5)^2+14.5$

$=-2(x^2+2.25+1.5x)+14.5$

$=-2x^2-4.5-3x+14.5$

$=-2x^2-3x+10$

This is the equation given in question.

4. ## Re: Issue with Converting to Standard Form

Originally Posted by deesuwalka

on expanding the answer you get

$-2(x+1.5)^2+14.5$

$=-2(x^2+2.25+1.5x)+14.5$

$=-2x^2-4.5-3x+14.5$

$=-2x^2-3x+10$

This is the equation given in question.
No, you are incorrect.
$(x+1.5)^2$ is not equal to $x^2+2.25+1.5x$, it is equal to $x^2+ 2.25+ 3.0x$.

(I would have written it $\displaystyle x^2+ 3.0x+ 2.25$ : $\displaystyle (x+ a)^2= x^2+ 2ax+ a^2$ not $\displaystyle x^2+ ax+ a^2$.

5. ## Re: Issue with Converting to Standard Form

Originally Posted by jennasam400
I have this problem. Convert to standard form.

-2x2-6x+10
The answer I come up with does not work when I check my work. What did I do wrong?
-2(x+1.5)2+14.5
I have a naive question. Who or what determines standard form?

6. ## Re: Issue with Converting to Standard Form

Originally Posted by Plato
I have a naive question. Who or what determines standard form?
From my experience, most secondary algebra texts have standard form as $y=ax^2+bx+c$. The same texts usually name $y=a(x-h)^2+k$ as the vertex form.

I have seen the vertex form called standard form in other sources. I've also seen $y=ax^2+bx+c$ called the general form.

Depends on the text, I guess.

7. ## Re: Issue with Converting to Standard Form

Originally Posted by HallsofIvy
No, you are incorrect.
$(x+1.5)^2$ is not equal to $x^2+2.25+1.5x$, it is equal to $x^2+ 2.25+ 3.0x$.

(I would have written it $\displaystyle x^2+ 3.0x+ 2.25$ : $\displaystyle (x+ a)^2= x^2+ 2ax+ a^2$ not $\displaystyle x^2+ ax+ a^2$.
Yes, I've mistakenly typed. thanks