Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Family of Parabolas

The equation y = (x - c)^2 defines a family of parabola, one parabola for each value of c. On the set of coordinate axes, graph the members of the family for c = 0, c = 3, and c = -2.

Let me see.

In other words, I am to graph the following parabolas:

y = (x - 0)^2

y = (x - 3)^3

y = (x -(-2))^2 = (x + 2)^2

Correct?

If so, Bob can you please graph each parabola using a different color.

What is the purpose for asking this question besides graphing 3 parabola?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Family of Parabolas

Knowing about 'families' of curves with similar properties helps a lot with curve sketching. Once you've got one sorted the rest are easy.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Family of Parabolas

https://i.imgur.com/1afdOAq.gif

Knowing about 'families' of curves with similar properties helps a lot with curve sketching. Once you've got one sorted the rest are easy.

Bob

Thank you for the beautiful graph. Students today don't know how to graph by hand. I haven't graphed by hand since my school days back in the 90s. I also feel there is no need to graph by hand with so many apps, online calculators and websites that do all the graphing needed.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Family of Parabolas

I have software. I couldn't make such smooth curves by hand.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Family of Parabolas

I have software. I couldn't make such smooth curves by hand.

Bob

I know that you have software. I thank you. In the old days, I had to graph by hand.