Graphing a parabola for a calculus problem

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Homework Help Overview

The discussion revolves around graphing a parabola defined by the equation y=4x^2 - 25, within the context of a calculus problem. Participants are exploring the characteristics of the parabola, including its x-intercepts and vertex.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss factoring the quadratic to find x-intercepts and mention the importance of identifying the turning point. There is uncertainty regarding the role of the coefficient in front of x^2 and how it affects the graph.

Discussion Status

Some participants have provided guidance on factoring and finding the turning point through the derivative. However, there is still confusion regarding the vertex's coordinates and the implications of the coefficient in the equation.

Contextual Notes

There is a mention of the need to clarify the vertex's position, as one participant corrects another's interpretation of the vertex's y-coordinate. The discussion reflects a mix of understanding and uncertainty about the graphing process.

hotrocks007
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I am graphing a parabola for a calculus problem. I understand how you factor and use the two x values as your x-intercepts, but I'm not sure how this one would be graphed.

y=4x^2 - 25. I understand how the vertex of the parabola would be at negative 25, but I have no clue what to do woith the 4x^2.
Help would be appreciated. thanks.
 
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Well, like you said factoring and getting the two x-intercepts is a start. You also want to know the turning point. If you don't remember the formula for that, just remember that the derivative is zero at the turning point and solve.
 
factoring you get (2x-5) (2x+5) set these equal to zero
 
By the way, the vertex is not "at negative 25"- that's just the y-value of the point. The vertex is at (0, -25).
 

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