Question

How do you find two quadratic function one that opens up and one that opens downward whose graphs have intercepts (0,0), (10,0)?

Answer 1

`f_"up"(x) = x^2-10x`

`f_"down"(x) = -x^2+10x`

Explanation:

Any quadratic function with these `x` intercepts is expressible in the form:

`f(x) = ax(x-10) = ax^2-10ax" "` for some constant `a != 0`

It must take this form in order that `f(0) = 0` and `f(10) = 0`.

If `a > 0` then this will open upwards and if `a < 0` then it will open downwards.

So we can use `a=+-1` to define the functions:

`f_"up"(x) = x^2-10x`

`f_"down"(x) = -x^2+10x`