Advanced Math/parabola

Advertisement

Expert: Robi Bhattacharjee - 9/17/2008


Question
Hi, there's a graph to this question, but i don't know how to draw it here so i'll try my best to describe it.
First of all the question: The graph below is a parabola that is symmetric about the x-axis. What is the equation of this parabola?

The graph is a "sideways" parabola with an opening to the right. One a paired of sets is given, it is the vertex of the parabola which is (-2, O).

The correct answer is x=y^2-2. I don't know how they got this answer. thanks again!

Answer
Hi Emily,

I'm terribly sorry for taking so much time to answer. I've had a lot of work lately.

For sideways parabola, you know the standard equation is x = ay^2 + by + c. If it symmetric about the x-axis, that means that b = 0. This is because when you say it is symmetric, you can stick in (-y) for y.

so ay^2 + by + c = a(-y)^2 + b(-y) + c

so by = -by          since y^2 = (-y)^2.

and this is for all y, so b must equal 0.

so your equation as form x = ay^2 + c.

Now you know it goes through (-2,0). So a(0)^2 + c = -2

so c = -2.

Now it has form x = ay^2 - 2.

If you look at the graph, by seeing points, you should be able to find out what a is. So as an exercise, try and see if you can understand why a is one.

I hope this helped,

Robi

Advanced Math

All Answers

Answers by Expert:

Ask Experts

Volunteer

Robi Bhattacharjee

Expertise

I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

Organizations
I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

©2012 About.com, a part of The New York Times Company. All rights reserved.