How does the second term in a quadratic, bx, affect the graph?

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Discussion Overview

The discussion centers around the impact of the linear term, bx, in a quadratic equation on the graph of the function. Participants explore various methods to understand this effect, including plotting different quadratics and relating the concept to kinematics.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant suggests experimenting by plotting quadratics with varying linear terms to observe their effects on the graph.
  • Another participant proposes considering the kinematic analogue, linking the quadratic's linear term to one-dimensional projectile motion.
  • A suggestion is made to complete the square on the general form of the quadratic equation, ax^2 + bx + c, to gain insights into the graph's transformations.
  • One participant agrees with the suggestion to complete the square, indicating it could clarify the relationship between the graph's translations and the formula transformations.
  • A later reply expresses gratitude for the helpfulness of the suggestions provided.

Areas of Agreement / Disagreement

Participants generally agree on the usefulness of experimentation and mathematical manipulation to understand the effects of the linear term, but no consensus on a single approach is reached.

Contextual Notes

The discussion does not resolve specific mathematical steps or assumptions related to the transformations of the quadratic function.

Fletcher
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How does the second term in a quadratic, bx, affect the graph?
 
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You could experiment with it! You're curious as to the effect of the linear term... so plot a bunch of quadratics with different linear terms.
 
Since this is physicsforum.com, you might also try to consider the kinematic analogue (representing one-dimensional projectile motion).
 
Or, try getting the general form, ax^2 + bx+c, and complete the square on that.
 
Yeah Gib, that's what I would suggest. If Fletcher knows how translations of the graph of a function are related to transformations of its formula, then completing the square will tell the him exactly what he wants to know.
 
Thanks, that was helpful.
 

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