# Completing the square

• Oct 18th 2012, 07:06 PM
Eraser147
Completing the square
I do not understand this at all. Click image to enlarge Attachment 25278. I keep getting the answer $\displaystyle 5(t-8/5)^2+1/5$, which means that the vertex of this equation is NOT $\displaystyle (8/5,-64/25)$. I even used h:$\displaystyle 8/5$ to plug it into the entire equation $\displaystyle 5t^2-16t+13$.
• Oct 18th 2012, 07:19 PM
topsquark
Re: Completing the square
Your completing the square work is correct. (The answer in the "Click to enlarge" panel, that is.)

-Dan
• Oct 18th 2012, 07:38 PM
Eraser147
Re: Completing the square
Why? Why is the k value not 1/5?
• Oct 18th 2012, 07:38 PM
Eraser147
Re: Completing the square
Can you show me the steps for the solution so I can look at the mechanics of it?
• Oct 18th 2012, 08:14 PM
Prove It
Re: Completing the square
Quote:

Originally Posted by Eraser147
I do not understand this at all. Click image to enlarge Attachment 25278. I keep getting the answer $\displaystyle 5(t-8/5)^2+1/5$, which means that the vertex of this equation is NOT $\displaystyle (8/5,-64/25)$. I even used h:$\displaystyle 8/5$ to plug it into the entire equation $\displaystyle 5t^2-16t+13$.

\displaystyle \displaystyle \begin{align*} 5 \left[ \left( t - \frac{8}{5} \right) ^2 - \frac{64}{25} \right] &= 5 \cdot \left( t - \frac{8}{5} \right)^2 + 5 \cdot \left( -\frac{64}{25} \right) \\ &= 5\left( t - \frac{8}{5} \right)^2 - \frac{64}{5} \end{align*}

So your turning point should be \displaystyle \displaystyle \begin{align*} \left( \frac{8}{5}, -\frac{64}{5} \right) \end{align*}.
• Oct 18th 2012, 08:42 PM
Eraser147
Re: Completing the square
It wouldn't make sense because if you plugin 8/5 into the original equation, 1/5 IS the answer for the k value.
• Oct 18th 2012, 09:06 PM
Prove It
Re: Completing the square
Quote:

Originally Posted by Eraser147
It wouldn't make sense because if you plugin 8/5 into the original equation, 1/5 IS the answer for the k value.

No amount of arguing is going to make your answer correct. You correctly completed the square, you did NOT do the expansion correctly.
• Oct 18th 2012, 09:55 PM
Eraser147
Re: Completing the square
No no no no, just no. That image is what the answer the solution manual has. THAT's NOT my answer. My answer is with the 1/5. I know how to expand, but no matter how I calculate it, it won't show the k value to have 1/5. Again, it is easily testable by jut plugging in k into the original polynomial above.