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

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The second term in a quadratic equation, bx, significantly influences the graph's shape and position. Experimenting with various linear terms can provide insights into these effects. Completing the square on the general form ax^2 + bx + c helps clarify how translations of the graph relate to transformations of the equation. Understanding these relationships is crucial for analyzing the graph's behavior, particularly in contexts like projectile motion. Overall, exploring these concepts through plotting and mathematical manipulation enhances comprehension of quadratic functions.
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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