Cubic and polynomial graphsIB MYP Maths Extended: Flashcards

What these 13 flashcards ask

What is a cubic function?
What does the sign of the x^3 term tell you?
How many roots can a cubic have?
How many turning points can a cubic have?
How do you find the roots of y=a(x-p)(x-q)(x-r)?
How do you find the y-intercept?
What does a repeated root do to the graph?
What is the degree of a polynomial?
What are the most roots and turning points of a degree n polynomial?
How do the ends of an even-degree graph behave?
How do you find a turning point with technology?
How do you solve f(x)=k with technology?
Why must you check the domain in a real-life cubic model?

Exam questions on Cubic and polynomial graphs

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).