# Thread: [SOLVED] parablas and factured form

1. ## [SOLVED] parablas and factured form

can all parablas be expressed in factered form
(explain with examples)

thank-you

2. Originally Posted by I_need_help
can all parablas be expressed in factered form
(explain with examples)

thank-you
You're from Canada? Then you should know that it's "parabola" and "factor."

It depends on what you want. You can always put a parabola into the vertex form:
$\displaystyle y = a(x - h)^2 + k$
if you would consider that factored.

However, if you are given $\displaystyle y = ax^2 + bx + c$, where a, b, and c are integers, and want to write it as $\displaystyle y = (dx + e)(fx + g)$

then the answer is, in general, no if you are talking about integer d, e, f, and g.

Ex:
$\displaystyle y = x^2 + x + 1$

There are not even any real numbers d, e, f, and g such that the right hand side factors.

-Dan

3. Originally Posted by I_need_help
can all parablas be expressed in factered form
(explain with examples)

thank-you
If they could, do you see why this would mean that all parabolas cut the horizontal axis (this axis is often called the x-axis) ..... Do they?

4. Originally Posted by I_need_help
can all parabolas be expressed in factered form
...
Hello,

of course not!

There are a lot more parabolas than those which are graphs of functions.

5. Originally Posted by earboth
Hello,

of course not!

There are a lot more parabolas than those which are graphs of functions.
Boy oh boy! You've really exponentialised this poor guy's worries now!!

I get the feeling all was meant to be qualified with the equation $\displaystyle y = ax^2 + bx + c$ ......