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

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Discussion Overview

The discussion centers around the graphing of the quadratic equation x^2 - 4x + 3 and the question of whether -4x can be considered a slope. Participants explore methods for graphing the equation without using a calculator or plotting points directly.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • Some participants assert that -4x is not a slope, explaining that the slope of a line is a constant number and that the given equation represents a parabola, which does not have a single slope.
  • One participant suggests completing the square as a method to clarify the graph's relationship to the standard form of a parabola.
  • Another participant shares a method of generating x-y values to plot points for the graph, providing specific values for x and their corresponding y outputs.
  • Some participants discuss the vertex form of the parabola and the significance of the vertex in graphing the equation.
  • There is a mention of learning methods for graphing in different educational contexts, indicating varying levels of familiarity with the concepts among participants.

Areas of Agreement / Disagreement

Participants generally agree that the graph is a parabola and that -4x is not a slope. However, there are differing opinions on the best methods for graphing the equation without using a calculator or plotting points directly, indicating a lack of consensus on the approach.

Contextual Notes

Some methods discussed, such as completing the square and generating x-y values, depend on familiarity with algebraic techniques and may not be universally applicable to all participants. The discussion reflects varying levels of mathematical background and understanding among participants.

ocean09
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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!
 
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Do you know what kind of shape the graph has?
 
Yes, a parabola.
 
You might try completing the square, this should make it clear how it relates to the graph of the good old y=x^2.
 
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.
 
HallsofIvy said:
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?
 
ocean09 said:
How would you graph this equation w/out plugging in points or using a calculator?

Why would you want to graph it?
 
b/c i want to know how to graph it :smile:
 
ocean09 said:
b/c i want to know how to graph it :smile:

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.
 
  • #10
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.
 
  • #11
HallsofIvy said:
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.
 
Last edited:

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