Cubic and polynomial graphsIB MYP Maths Extended: Mind map

Exam questions on Cubic and polynomial graphs

1. Consider the cubic function $f(x)=(x+2)(x-1)(x-3)$.
   Write down the values of $x$ for which $f(x)>0$.2 marks
2. Consider the cubic function $g(x)=x^3-4x$.
   Use technology to find the coordinates of the local minimum point of the graph of $y=g(x)$. Give each coordinate to 3 significant figures.2 marks
3. Sam investigates the family of cubic graphs $y=x^3-kx$ for different positive values of $k$. Using graphing software, Sam finds that for $k=1$ the graph crosses the $x$-axis at $-1$, $0$ and $1$; for $k=4$ it crosses at $-2$, $0$ and $2$; and for $k=9$ it crosses at $-3$, $0$ and $3$.
   Describe the pattern in the $x$-intercepts of $y=x^3-kx$ and write a general rule for them in terms of $k$. Verify your rule for $k=16$.3 marks