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

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SUMMARY

The second term in a quadratic equation, represented as bx, significantly influences the graph's shape and position. Experimenting with various linear terms in the general form ax^2 + bx + c allows for a deeper understanding of its effects. Completing the square provides insights into how translations of the graph relate to transformations of the formula. This method is particularly useful for visualizing the impact of the linear term on the graph's behavior.

PREREQUISITES
  • Understanding of quadratic equations in the form ax^2 + bx + c
  • Familiarity with the concept of completing the square
  • Basic knowledge of graph transformations
  • Experience with plotting functions using graphing tools
NEXT STEPS
  • Explore the process of completing the square for quadratic equations
  • Learn how to plot quadratic functions using graphing software
  • Investigate the relationship between linear terms and graph translations
  • Study kinematic equations related to one-dimensional projectile motion
USEFUL FOR

Students, educators, and anyone interested in understanding the graphical representation of quadratic equations and their applications in physics and mathematics.

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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