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Sketch the graph of a polynomial:
Solution:
Consider the given equation above
Did you notice that the given equation is a perfect trinomial square? 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 1.
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(+)² = (+)
If 0 < x < 1, then y = (-)²(+)² = (+)
If x > 1, then y = (+)²(+)² = (+)
Here's the graph of a polynomial:
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| Photo by Math Principles in Everyday Life |
