Answer: Is -4x a slope? Graph x^2-4x+3

[ocean09]

Graph x^2-4x+3.

My question:

1) is -4x a slope?

I'm trying to graph this equation w/out using a calculator or plugging in points.


Thanks!

 

[Hurkyl]

Do you know what kind of shape the graph has?

 

[ocean09]

Yes, a parabola.

 

[shmoe]

You might try completing the square, this should make it clear how it relates to the graph of the good old y=x^2.

 

[HallsofIvy]

No, "-4x" is not a slope. The slope of a line is a number. If y= mx+ b then the slope is the number m. In the example given, y=x²- 4x+ 3, the graph is not a line and so doesn't have a slope. One definition of "derivative" is that the derivative, at any given value of x, is the slope of the tangent line.

 

[ocean09]

No, "-4x" is not a slope. The slope of a line is a number. If y= mx+ b then the slope is the number m. In the example given, y=x²- 4x+ 3, the graph is not a line and so doesn't have a slope. One definition of "derivative" is that the derivative, at any given value of x, is the slope of the tangent line.

How would you graph this equation w/out plugging in points or using a calculator?

 

[CRGreathouse]

How would you graph this equation w/out plugging in points or using a calculator?

Why would you want to graph it?

 

[ocean09]

b/c i want to know how to graph it

 

[d_leet]

b/c i want to know how to graph it

You know that it looks like a parabola. Are you familiar with the vertex form of the equation for a parabola? If so then doing what shmoe suggested would help you graph it.

 

[HallsofIvy]

Well, I think it was in fifth grade where they taught me to make a list of x y values:

x y= x²- 4x+ 3
0 3
1 1- 4+ 3= 0
-1 1+ 4+ 3= 8
2 4- 8+ 3= -1
-2 4+ 8+ 3= 15
3 9- 12+ 3= 0
-3 9+ 12+3= 24
etc, mark the points (0,3), (1, 0), (-1, 8), (2, -1), (-2, 15), (3, 0), (-3, 24) and then draw a smooth curve through the points.

Another method, that I think I didn't learn until 9th or 10th grade was to complete the square: if y= x²- 4x+ 3= x²- 4x+ 4- 4+ 3= (x- 2)²- 1. The graph is a parabola with vertex (2, -1) opening upward.

 

[ocean09]

Another method, that I think I didn't learn until 9th or 10th grade was to complete the square: if y= x²- 4x+ 3= x²- 4x+ 4- 4+ 3= (x- 2)²- 1. The graph is a parabola with vertex (2, -1) opening upward.

i was looking through my math book, and it showed me how to graph it.

it doesn't hurt to sound stupid sometimes. at least, you are learning something.