# Translation difficulties with quadratic example

• Mar 20th 2011, 01:30 PM
Zellator
Hi Math Help Forum! (Bow)

I'm having problems in English written exercises, such as:

The quadratic function which takes the value \$\displaystyle 41\$ at \$\displaystyle x=-2\$ and the value \$\displaystyle 20\$ at \$\displaystyle x=5\$ and is minimized at \$\displaystyle x=2\$ is:

And the minimum value of this function is:

So, what does "minimized at" means in this problem? The vertex of the function?

It would be extremely helpful if someone do the steps for this one too! :3

Salutations from Brazil! :3
• Mar 20th 2011, 01:42 PM
skeeter
Quote:

Originally Posted by Zellator
Hi Math Help Forum! (Bow)

I'm having problems in English written exercises, such as:

The quadratic function which takes the value \$\displaystyle 41\$ at \$\displaystyle x=-2\$ and the value \$\displaystyle 20\$ at \$\displaystyle x=5\$ and is minimized at \$\displaystyle x=2\$ is:

And the minimum value of this function is:

So, what does "minimized at" means in this problem? The vertex of the function? yes

It would be extremely helpful if someone do the steps for this one too! :3

Salutations from Brazil! :3

equation for a quadratic with vertex \$\displaystyle (h,k)\$ is ...

\$\displaystyle y = a(x - h)^2 + k\$

you are given \$\displaystyle h = 2\$ , \$\displaystyle a > 0\$

use the \$\displaystyle (x,y)\$ coordinates of the two given points to determine \$\displaystyle a\$ and \$\displaystyle k\$
• Apr 3rd 2011, 11:58 AM
Zellator
Quote:

Originally Posted by skeeter
equation for a quadratic with vertex \$\displaystyle (h,k)\$ is ...

\$\displaystyle y = a(x - h)^2 + k\$

you are given \$\displaystyle h = 2\$ , \$\displaystyle a > 0\$

use the \$\displaystyle (x,y)\$ coordinates of the two given points to determine \$\displaystyle a\$ and \$\displaystyle k\$

Hi Skeeter!

Thank you so much for the reply!
I've been very busy so I only got to respond now. :3

So, the question was REALLY easy, wasn't it?

Wolfram confirms the answer as \$\displaystyle y=3x^2-12x-19\$.

After getting \$\displaystyle a\$ and \$\displaystyle k\$ I got to resolve it with \$\displaystyle Xv=-b/(2a)\$ and \$\displaystyle Yv=-(b^2-4ac)/(4a)\$.
No problem with this method, but do you know any other ways to resolve this?
It seem to be simpler than that.