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

I have the first point is (0, -100) and the second point is (7500, -250), and the maximum point is at (x, 210).

Is it possible to find X or the equation of the parabola using this information alone?

If so how?

share|cite|improve this question
Parabolas don't have a "first" and "last" point. Presumably, you are talking about a portion of the parabola. – Arturo Magidin Mar 15 '11 at 4:13
I am talking about where it crosses the x axis. I edited the question to reflect that. – garbagecollector Mar 15 '11 at 4:14
@garbagecollector: Neither $(0,-100)$ nor $(7500,-250)$ are on the $x$-axis, so how could they possibly be the intersections of the parabola with the $x$-axis? – Arturo Magidin Mar 15 '11 at 4:19
@Arutro I edited the wrong question on accident. – garbagecollector Mar 15 '11 at 4:22
@garbagecollector: Parabolas still don't have a "first" or "last" point. They are infinite curves. – Arturo Magidin Mar 15 '11 at 4:24

Assume you have $y=ax^2 + bx + c$. The maximum is achieved at $x = -\frac{b}{2a}$.

The values you have give you the value of $c$ ($-100$), and a relation between $a$ and $b$ obtained by plugging in $(7500,-250)$. You also know that the maximum is achieved at $-\frac{b}{2a}$, so plugging that will give you another relation between $a$ and $b$. Putting them together will give you a quadratic equation that $b$ must satisfied.

share|cite|improve this answer

Three points determine a parabola, since you have three constants to account for in $y=ax^2+bx+c$ . Construct the appropriate system of linear equations and you're golden.

Otherwise, if you're too cool for solving linear equations, there is a determinant expression for the parabola passing through three points $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$:


whose verification is left as an exercise.

share|cite|improve this answer
I have updated the question. Could you update your answer to reflect it. – garbagecollector Mar 15 '11 at 4:17
$(7500, -250)$ ain't an x-intercept, yo. ;) The quadratic formula is excellent for figuring where a parabola crosses the horizontal axis, tho. – user8276 Mar 15 '11 at 4:20
I accidentally edited the wrong question. If you could answer it as written now. It would be appreciated. – garbagecollector Mar 15 '11 at 4:24

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.