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Sketch the graph of a polynomial:
Solution:
Consider the given equation above
Did you notice that the given equation can be factored by grouping? Let's factor the above equation as follows
and then it is factorable by the difference of two cubes as follows
If we set y = 0, then we can solve for the value of x at each factors which are the x-intercepts.
For
, the value of x is
For
, the value of x is
Since the roots of the second factor are imaginary numbers, then we cannot accept those values. Because of this, the only x-intercept is 2.
If we set x = 0, the y-intercept of the given equation is
Since we now the x-intercept, then we can sketch the location or direction of a curve as follows
If x < 0, then y = (-)²(+) = (+)
If 0 < x < 2, then y = (-)²(+) = (+)
If x > 2, then y = (+)²(+) = (+)
Here's the graph of a polynomial:
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| Photo by Math Principles in Everyday Life |