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### Graphing a Parabola

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Date: 3 Apr 1995 18:53:03 -0400
From: Anonymous
Subject: quadratic equations

Dear Dr. Math,
I'm doing my homework and I don't understand how to do
this problem, and I was hoping you could show me.  How
do you graph the quadratic equation, y=3(x+1)^2 - 20?
Thanks for your help.

your pal,
cornfed9 (screen name)
```

```
Date: 3 Apr 1995 20:24:35 -0400
From: Dr. Ken
Subject: Re: quadratic equations

Hello there!

When doing this kind of problem, it helps to have an idea
what the standard parabola y=x^2 looks like; I'm sure you've
seen it.  Then you see how your equation differs from the
standard, piece by piece.

So in your case, let's build up your equation.  If it were
y = (x+1)^2, it would just be the standard parabola, but
moved to the left one unit.  Then we multiply by 3, which
takes the whole thing and makes it three times as tall and
skinny.  Then when you subtract 20 to get 3(x+1)^2 - 20, the
whole picture moves down 20 units.  Then you're done.

So this is a parabola centered at (-1, -20), and three times
as tall & skinny as the standard parabola.  Hope this helps.

-Ken "Dr." Math
```
Associated Topics:
High School Equations, Graphs, Translations

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