# Writing a function in standard form

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• Feb 28th 2011, 02:48 PM
SquawkVFR
Writing a function in standard form
Express the function 'f' in standard form:
-2x^2 - 6x + 3

I've got:
(-2x^2 - 6x/2 + 36/4) + 3
(-2x^2 - 3x + 9) + 3
-2(x^2 - 3x/-2 + 9/-2) + 3 - (9/-2)
= y=(x + 3/2)^2 + 15/2

I inputted the original function and the standard form into a graphing calculator and it came up with two different parabolas. Did I make an error in my math?
• Feb 28th 2011, 02:53 PM
topsquark
Quote:

Originally Posted by SquawkVFR
Express the function 'f' in standard form:
-2x^2 - 6x + 3

I've got:
(-2x^2 - 6x/2 + 36/4) + 3
(-2x^2 - 3x + 9) + 3
-2(x^2 - 3x/-2 + 9/-2) + 3 - (9/-2)
= y=(x + 3/2)^2 + 15/2

I inputted the original function and the standard form into a graphing calculator and it came up with two different parabolas. Did I make an error in my math?

Okay, there are some notational problems going on here. This is the way I would recommend doing this.

$\displaystyle -2x^2 - 3x + 3$

$\displaystyle (-2x^2 - 3x) + 3$

$\displaystyle -2 \left ( x^2 + \frac{3}{2} x \right ) + 3$

$\displaystyle -2 \left ( x^2 + \frac{3}{2} x + \left [ \frac{9}{4} \right ] - \left [ \frac{9}{4} \right ] \right ) + 3$

$\displaystyle -2 \left ( x^2 + \frac{3}{2} x + \left [ \frac{9}{4} \right ] \right ) - (-2) \cdot \left [ \frac{9}{4} \right ] + 3$

$\displaystyle -2 \left ( x + \frac{3}{2} \right ) ^2 + \frac{15}{2}$

-Dan