IB Mathematics Analysis and Approaches Question Type 1: Graphing Simple Polynomials Up to the 3rd Degree Exercises

Solve the inequality $(x-4)(x-3)(x-2)>(x-1)(x-3)(x-2)$.

Show that the inflection point of $y=(x-1)(x-2)(x-3)$ occurs at $x=2$ and find its $y$-coordinate.

Calculate the $y$-values at the turning points of the function $y=(x-4)(x-3)(x-2)$.

Sketch the graph of $y=(x-1)(x-3)(x-2)$. Identify its $x$-intercepts and state the sign of $y$ in each interval determined by the roots.

Express $(x-4)(x-3)(x-2)-(x-1)(x-3)(x-2)$ in fully factored form.

Determine the $x$- and $y$-intercepts of the curve $y=(x-4)(x-3)(x-2)$.

Determine the intervals where $f(x)=(x-4)(x-3)(x-2)$ is increasing and where it is decreasing.

Solve the equation $(x-4)(x-3)(x-2)-(x-1)(x-3)(x-2)=2$.

Find the coordinates of the turning points of $y=(x-1)(x-3)(x-2)$.

Sketch the graph of $y=(x-4)(x-3)(x-2)$. Identify its $x$-intercepts and describe its end behavior.

Solve the equation $(x-4)(x-3)(x-2)=(x-1)(x-3)(x-2)$.

Compare the end behavior of the two polynomials $y_1=(x-4)(x-3)(x-2)$ and $y_2=(x-1)(x-3)(x-2)$.