Graph y=x^4 - 3x^2 + 2 & Find x-intercepts

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Homework Help Overview

The discussion revolves around the graphing of the function y=x^4 - 3x^2 + 2, specifically focusing on identifying and labeling the x-intercepts. The subject area includes polynomial functions and their graphical representations.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore different methods to analyze the polynomial, including factoring and completing the square. Questions arise regarding the steps needed to find the x-intercepts and how to effectively sketch the graph.

Discussion Status

Some participants have suggested methods such as factoring and completing the square, while others mention using synthetic division. There is an ongoing exploration of these approaches without a clear consensus on the best method to proceed.

Contextual Notes

Participants are discussing the equation under the constraints of homework guidelines, which may limit the extent of assistance provided. The original poster's request for exact values indicates a need for precision in the solution process.

rachael
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Sketch the graph, labelling the x-intercepts with exact values

how do i work this equation out?

y=x^4 - 3x^2 + 2
 
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rachael said:
Sketch the graph, labelling the x-intercepts with exact values

how do i work this equation out?

y=x^4 - 3x^2 + 2

This equation is known as a "biquadratic." It factors. If it helps, set a=x^2 and take a look at it again.

-Dan
 
thank you
so the new equation would be
a^2 - 3a + 2
then use the rule 'completing the square'
 
You could factor it using synthetic division. Once you find its factors, you can plot the points, test for sign changes, and sketch it as usual.
 

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