Question

I award medals!!

Please give me an example of a function with two real rational solutions. I would like the function to be f(x) please. I am trying to grasp what my math lesson is teaching me but the examples aren't that great.

Answer 1

@timaashorty @marylou004 @phi

Answer 2

fx)= (x-1)(x-2)

has two solutions to f(x)=0

but can you post what the lesson is saying ?

Answer 3

but I don't really think that is what the question is looking for.

Answer 4

I reread the lesson and cant find anything on it. I looked at the examples but they don't have equations like the one you posted

Answer 5

can you post one of the examples?

Answer 6

I cannot tell for sure, but it looks like they are translating a quadratic from standard form to "vertex form"
see http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php

if so, you would do this:

\[ f(x)= x^2+12x +26 \\\text{ change f(x) to y}\\
y= x^2+12x +26 \\
\text{add } \left(\frac{12}{2}\right)^2 \text{ to both sides}\\
y+36= x^2+12x +36 +26 \\
\]
rewrite \( x^2+12x +36 \) as \( (x+6)^2 \)
\[ y+36= (x+6)^2+26 \]
add -36 to both sides to get vertex form
\[ y= (x+6)^2 -10 \]

Answer 7

oh okay. That's easy enough.

Answer 8

Thank you :-)