1. ## Translation difficulties with quadratic example

Hi Math Help Forum!

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

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

2. Originally Posted by Zellator
Hi Math Help Forum!

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

The quadratic function which takes the value $41$ at $x=-2$ and the value $20$ at $x=5$ and is minimized at $x=2$ 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 $(h,k)$ is ...

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

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

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

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

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

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

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

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 $y=3x^2-12x-19$.

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

About the formula $y=a(x-h)^2+k$.
I've never ever seen this, or someone using it whatsoever.
I get it, education is kind of lousy in here. It's a basic Algebra II formula isn't?
I feel so embarrassed hahahahah :3

Thanks Again Skeeter!