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Sketch the graph of a polynomial:
Solution:
Consider the given equation above
Did you notice that the trinomial inside the parenthesis is factorable by the product of two binomials? Let's factor the above equation as follows
If we set y = 0, then the x-intercepts of the given equation are 3, and -1.
If we set x = 0, then 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 < -1, then y = (-)²(-)² = (+)
If -1 < x < 0, then y = (-)²(+)² = (+)
If 0 < x < 3, then y = (-)²(+)² = (+)
If x > 3, then y = (+)²(+)² = (+)
Here's the graph of a polynomial:
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| Photo by Math Principles in Everyday Life |