Editing Polynomial (section)

=== Graphs ===
<div class="floatright">
<gallery perrow="2" widths="120px" heights="120px">
File:Algebra1 fnz fig037 pc.svg|Polynomial of degree 0:<br/><small>{{math|''f''(''x'') {{=}} 2}}</small>
File:Fonction de Sophie Germain.png|Polynomial of degree 1:<br/><small>{{math|''f''(''x'') {{=}} 2''x'' + 1}}</small>
File:Polynomialdeg2.svg|Polynomial of degree 2:<br/><small>{{math|''f''(''x'') {{=}} ''x''<sup>2</sup> − ''x'' − 2}}<br/>{{math|{{=}} (''x'' + 1)(''x'' − 2)}}</small>
File:Polynomialdeg3.svg|Polynomial of degree 3:<br/><small>{{math|''f''(''x'') {{=}} ''x''<sup>3</sup>/4 + 3''x''<sup>2</sup>/4 − 3''x''/2 − 2}}<br/>{{math|{{=}} 1/4 (''x'' + 4)(''x'' + 1)(''x'' − 2)}}</small>
File:Polynomialdeg4.svg|Polynomial of degree 4:<br/><small>{{math|''f''(''x'') {{=}} 1/14 (''x'' + 4)(''x'' + 1)(''x'' − 1)(''x'' − 3) <br/>+ 0.5}}</small>
File:Quintic polynomial.svg|Polynomial of degree 5:<br/><small>{{math|''f''(''x'') {{=}} 1/20 (''x'' + 4)(''x'' + 2)(''x'' + 1)(''x'' − 1)<br/>(''x'' − 3) + 2}}</small>
File:Sextic Graph.svg|Polynomial of degree 6:<br/><small>{{math|''f''(''x'') {{=}} 1/100 (''x''<sup>6</sup> − 2''x'' <sup>5</sup> − 26''x''<sup>4</sup> + 28''x''<sup>3</sup>}}<br/>{{math|+ 145''x''<sup>2</sup> − 26''x'' − 80)}}</small>
File:Septic graph.svg|Polynomial of degree 7:<br/><small>{{math|''f''(''x'') {{=}} (''x'' − 3)(''x'' − 2)(''x'' − 1)(''x'')(''x'' + 1)(''x'' + 2)}}<br/>{{math|(''x'' + 3)}}</small>
</gallery>
</div>
A polynomial function in one real variable can be represented by a [[graph of a function|graph]].
<ul>
<li>
The graph of the zero polynomial
{{block indent|{{math|1=''f''(''x'') = 0}}}} is the {{math|''x''}}-axis.
</li>
<li>
The graph of a degree 0 polynomial
{{block indent|{{math|1=''f''(''x'') = ''a''<sub>0</sub>}}, where {{math|''a''<sub>0</sub> ≠ 0}},}} is a horizontal line with {{nowrap|{{math|''y''}}-intercept {{math|''a''<sub>0</sub>}}}}
</li>
<li>
The graph of a degree 1 polynomial (or linear function)
{{block indent|{{math|1=''f''(''x'') = ''a''<sub>0</sub> + ''a''<sub>1</sub>''x''}}, where {{math|''a''<sub>1</sub> ≠ 0}},}} is an oblique line with {{nowrap|{{math|''y''}}-intercept {{math|''a''<sub>0</sub>}}}} and [[slope]] {{math|''a''<sub>1</sub>}}.
</li>
<li>
The graph of a degree 2 polynomial
{{block indent|{{math|1=''f''(''x'') = ''a''<sub>0</sub> + ''a''<sub>1</sub>''x'' + ''a''<sub>2</sub>''x''<sup>2</sup>}}, where {{math|''a''<sub>2</sub> ≠ 0}}}} is a [[parabola]].
</li>
<li>
The graph of a degree 3 polynomial
{{block indent|{{math|1=''f''(''x'') = ''a''<sub>0</sub> + ''a''<sub>1</sub>''x'' + ''a''<sub>2</sub>''x''<sup>2</sup> + ''a''<sub>3</sub>''x''<sup>3</sup>}}, where {{math|''a''<sub>3</sub> ≠ 0}}}} is a [[cubic equation|cubic curve]].
</li>
<li>
The graph of any polynomial with degree 2 or greater
{{block indent|{{math|1=''f''(''x'') = ''a''<sub>0</sub> + ''a''<sub>1</sub>''x'' + ''a''<sub>2</sub>''x''<sup>2</sup> + ⋯ + ''a''<sub>''n''</sub>''x''<sup>''n''</sup>}}, where {{math|''a''<sub>''n''</sub> ≠ 0 and ''n'' ≥ 2}}}} is a continuous non-linear curve.
</li>
</ul>

A non-constant polynomial function [[infinity#Calculus|tends to infinity]] when the variable increases indefinitely (in [[absolute value]]). If the degree is higher than one, the graph does not have any [[asymptote]]. It has two [[parabolic branch]]es with vertical direction (one branch for positive ''x'' and one for negative ''x'').

Polynomial graphs are analyzed in calculus using intercepts, slopes, concavity, and end behavior.