Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Can you help me find the answer to this question?

For any real number $\alpha$, the parabola $f_{\alpha}(x) = 2x^2 + \alpha x + 3\alpha$ passes through the common point $(a, b)$. What is the value of $a + b$?

share|cite|improve this question
Could you please use LaTeX to make your question readable? It is not very clear whether you meant to write $\,f(x)\,$ or $\,f(\alpha x)\,$ , for example. you use the FAQ section to get directions on this. – DonAntonio Nov 29 '12 at 13:08
Wow! Great guessing work, @Michael Albanese ! – DonAntonio Nov 29 '12 at 13:16
up vote 2 down vote accepted

So for any $\,\alpha\in\Bbb R\,$ ,we have that

$$b=f_\alpha(a)=2a^2+a\alpha+3\alpha\Longrightarrow $$

Since this is true for any $\,\alpha\in\Bbb R\,$ , let us choose:

$$\;\;\;\;\;\;\;\;\;\;\;\;\;\begin{align*}(1)\;\;\;\alpha=0:& \,\,b=2a^2\\(2)\;\;\;\alpha=1:&\,\,b=2a^2+a+3\end{align*}$$

Comparing (1)-(2), we get

$$a+3=0\Longrightarrow a=-3\Longrightarrow b=2\cdot 3^2=18\Longrightarrow a+b=15$$

share|cite|improve this answer

Choose two values for $\alpha=0,1$ and set $f_0(x)=f_1(x)$ to get: $$ 2x^2=2x^2+x+3 \\ x+3=0 \rightarrow x=-3 \rightarrow y=2(-3)^2=18 $$ Then $x+y=-3+18=15$.

share|cite|improve this answer
Since I can only choose 1 answer I choose the other and upvoted you – chndn Dec 4 '12 at 11:54
@chndn fair enough... – draks ... Dec 4 '12 at 11:55

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.