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# Graph each polynomial function. Factor first if the expression is not in factored form. f(x)=(4x+3)(x+2)^{2} # Graph each polynomial function. Factor first if the expression is not in factored form. f(x)=(4x+3)(x+2)^{2}

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Polynomial graphs asked 2021-01-10
Graph each polynomial function. Factor first if the expression is not in factored form. $$\displaystyle{f{{\left({x}\right)}}}={\left({4}{x}+{3}\right)}{\left({x}+{2}\right)}^{{{2}}}$$

## Answers (1) 2021-01-11
Step 1 $$\displaystyle{f{{\left({x}\right)}}}={\left({4}{x}+{3}\right)}{\left({x}+{2}\right)}^{{{2}}}$$ The function has two zeros $$\displaystyle-{\frac{{{3}}}{{{4}}}},-{2}$$ So, the graph of f(x) crosses the x-axis at $$\displaystyle{\left({\frac{{{4}}}{{{3}}}},{0}\right)}$$ and $$\displaystyle{\left(-{2},{0}\right)}$$ To find the y-intercept, substitute 0 for x in f(x) $$\displaystyle{f{{\left({x}\right)}}}={\left({4}{x}+{3}\right)}{\left({x}+{2}\right)}^{{{2}}}$$
$$\displaystyle{f{{\left({0}\right)}}}={\left({4}{\left({0}\right)}+{3}\right)}{\left({0}+{2}\right)}^{{{2}}}$$ Substitute 0 for x Simplify $$\displaystyle={\left({3}\right)}{\left({2}\right)}^{{{2}}}$$
$$\displaystyle={12}$$ So, the function f(x) crosses the y-axis at (0,12) Step 2 $$\displaystyle{4}{x}\cdot{\left({x}\right)}^{{{2}}}={4}{x}^{{{3}}}$$ The leading coefficient is 4 Since the leading coefficient is positive and the function f(x) of degree 3 (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 ### Relevant Questions asked 2021-02-12
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