Math Is Fun Forum

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

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?

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,209

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

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

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.

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,209

Re: Family of Parabolas

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

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

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

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.

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah