7F - Families of quartic functions
Unlike quadratics, quartic functions do not have one standard shape when graphing. Instead, we need to consider several different cases based on the form of the equation:
\[y=a(x-h)^4+k\]
|
\[y=a(x-l)(x-m)(x-n)(x-p)\]
|
\[y=a(x-l)^2(x-m)(x-n)\]
|
\[y=a(x-m)^2(x-n)^2\]
|
\[y=a(x-m)^3(x-n)\]
|
\[y=(x-m)^2(ax^2+bx+c)\]
|
7F - Example 1: sKETCHING the graph of A QUARTIC function (CAS)
Sketch the graph of \(y=x^4-x^3-13x^2+x+12\) clearly labelling all axial intercepts and turning points with their coordinates. Where necessary, give the coordinates correct to two decimal places.
|
7F - Example 1: Video solution
7F - Example 1: Practice
Question 1: ABC Question 2: ABC 7F - Example 1: Solutions
Question 1: ABC Question 2: ABC |
7F - Example 2: sKETCHING the graph of A QUARTIC function
Sketch the graph of \(y=-(x-3)^4+16\). Clearly label any axial intercepts with their coordinates.
|
7F - Example 2: Video solution
7F - Example 2: Practice
Question 1: ABC Question 2: ABC 7F - Example 2: Solutions
Question 1: ABC Question 2: ABC |
7F - Example 3: sKETCHING the graph of A QUARTIC function
Sketch the graph of \(y=(2x+5)(x-3)^3\). Clearly label any axial intercepts with their coordinates.
|
7F - Example 3: Video solution
7F - Example 3: Practice
Question 1: ABC Question 2: ABC 7F - Example 3: Solutions
Question 1: ABC Question 2: ABC |
7F - Example 4: sKETCHING the graph of A QUARTIC function
Sketch the graph of \(y=-x^4+9x^2\). Clearly label any axial intercepts with their coordinates.
|
7F - Example 4: Video solution
7F - Example 4: Practice
Question 1: ABC Question 2: ABC 7F - Example 4: Solutions
Question 1: ABC Question 2: ABC |