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

  • Thread starter rachael
  • Start date
  • Tags
    Graphing
In summary, to graph the equation y=x^4 - 3x^2 + 2, first factor it into (x^2 - 2)(x^2 - 1). Then use the rule of completing the square or synthetic division to find the x-intercepts with exact values. Finally, plot the points and sketch the graph as usual.
  • #1
rachael
55
0
Sketch the graph, labelling the x-intercepts with exact values

how do i work this equation out?

y=x^4 - 3x^2 + 2
 
Physics news on Phys.org
  • #2
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
 
  • #3
thank you
so the new equation would be
a^2 - 3a + 2
then use the rule 'completing the square'
 
  • #4
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.
 

1. What is the equation being graphed?

The equation being graphed is y=x^4 - 3x^2 + 2.

2. How do you find the x-intercepts of the graph?

The x-intercepts can be found by setting y=0 and solving for x. In this case, we would set x^4 - 3x^2 + 2 = 0 and solve for x to find the x-intercepts.

3. How many x-intercepts does the graph have?

The graph can have a maximum of four x-intercepts, as it is a fourth degree polynomial. However, it is possible to have less than four x-intercepts depending on the values of the coefficients in the equation.

4. Can you provide an example of how to find the x-intercepts?

For example, if we have the equation y=x^4 - 3x^2 + 2, we can set y=0 and solve for x. This would give us the equation 0=x^4 - 3x^2 + 2. We can then factor this equation to get (x^2 - 2)(x^2 - 1) = 0. From here, we can solve for x to find the x-intercepts, which would be x=+/-√2 and x=+/-1.

5. What is the significance of the x-intercepts in this graph?

The x-intercepts represent the points where the graph of the equation intersects with the x-axis. These points have a y-coordinate of 0 and can provide information about the roots or solutions of the equation.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
10
Views
476
  • Precalculus Mathematics Homework Help
Replies
3
Views
907
  • Precalculus Mathematics Homework Help
Replies
4
Views
1K
  • Precalculus Mathematics Homework Help
Replies
7
Views
802
  • Precalculus Mathematics Homework Help
Replies
3
Views
722
  • Precalculus Mathematics Homework Help
Replies
4
Views
540
  • Precalculus Mathematics Homework Help
Replies
15
Views
498
  • Precalculus Mathematics Homework Help
Replies
4
Views
866
  • Precalculus Mathematics Homework Help
Replies
12
Views
912
  • Precalculus Mathematics Homework Help
Replies
19
Views
1K
Back
Top