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# Graph each polynomial function. Factor first if the expression is not in factored form. f(x)=x^{2}(x-5)(x+3)(x-1) # Graph each polynomial function. Factor first if the expression is not in factored form. f(x)=x^{2}(x-5)(x+3)(x-1)

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Polynomial graphs asked 2021-02-12
Graph each polynomial function. Factor first if the expression is not in factored form. $$\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}}{\left({x}-{5}\right)}{\left({x}+{3}\right)}{\left({x}-{1}\right)}$$

## Answers (1) 2021-02-13
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}}{\left({x}-{5}\right)}{\left({x}+{3}\right)}{\left({x}-{1}\right)}$$ The function in factored form The function has four zeros 0,5,-3 and 1. So, the graph of f(x) crossed the x-axis at (0,0), (5,0),(-3,0), and (1,0) To find the y-intercept, substitute 0 for x in f(x) $$\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}}{\left({x}-{5}\right)}{\left({x}+{3}\right)}{\left({x}-{1}\right)}$$
$$\displaystyle{f{{\left({0}\right)}}}={0}^{{{2}}}{\left({0}-{5}\right)}{\left({0}+{3}\right)}{\left({0}-{1}\right)}$$ Substitute 0 for x
$$\displaystyle={0}$$ So, the function f(x) crosses the y-axis at (0,0) Step 2 PSKx^{2}\cdot x \cdot x\cdot x=x^{5} The leading coefficient is 1 Since the leading coefficient is positive and the function f(x) of degree 5 (odd degree) So, the end behavior is $$\displaystyle{x}\rightarrow\infty,{f{{\left({x}\right)}}}\rightarrow\infty$$
$$\displaystyle{x}\rightarrow-\infty,{f{{\left({x}\right)}}}\rightarrow-\infty$$ See the graph below FZP https://q2a.s3-us-west-1.amazonaws.com/dev/1961020641.jpg"/>

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