Question 202897: A polynomial function f(x) has a zero of 3 with multiplicity 2. (1)since the zero is 3, the graph crosses the y-axis at 3? (2) since the zero is 3, the graph goes up to the right? (3) since the multiplicity is 2, the graph crosses the x-axis? (4) since the multiplicity is 2, the graph touches but does not cross the x-axis? Please help me with this!!!
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! A polynomial function f(x) has a zero of 3 with multiplicity 2.
The phrase "a function has a zero of a with a multiplicity of b" it means that the function, when factored, has "b" factors of (x-a). In other words, the function, when factored, has  in it. (There may be additional factors, too.) So your function, in factored form, includes  since it has a zero of 3 with a multiplicity of 2
(1)since the zero is 3, the graph crosses the y-axis at 3?
Zeros are x-values which cause the function to have a value of zero. So zeros are where the graph intersects the x-axis (where y-values are 0)
(2) since the zero is 3, the graph goes up to the right?
Zeros of any multiplicity have little to do with this. They are simply where the graph intersects the x-axis
(3) since the multiplicity is 2, the graph crosses the x-axis?
The graph intersects the x-axis at 3. But zeros of any even multiplicity do not cross from one side of the x-axis to the other.
(4) since the multiplicity is 2, the graph touches but does not cross the x-axis?
True. Zeros of even multiplicity mean there is a "bump" (either a u-like shape or an upside-down u-like shape) in the graph where just the tip of the "bump" touches the x-axis at that zero.
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