- #1
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
how do i work this equation out?
y=x^4 - 3x^2 + 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
The equation being graphed is y=x^4 - 3x^2 + 2.
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.
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.
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.
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.