Review question

# Can we compose these polynomial functions? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7553

## Suggestion

Let $f_n(x)=(2+(-2)^n)x^2+(n+3)x+n^2$ where $n$ is a positive integer and $x$ is any real number.

1. Write down $f_3(x)$.

Find the maximum value of $f_3(x)$.

For what values of $n$ does $f_n(x)$ have a maximum value (as $x$ varies)?

The green curve here is $y=(2+(-2)^n)x^2+(n+3)x+n^2$, where $n$ is a positive integer.

What happens as we vary $n$? Make sure you can explain algebraically the behaviour you can see here.