What does changing the "k" variable do to the graph of a quadratic?

I’ll be assuming you meant k as in
the a in a quadratic equation:

ax^2 + bx + c

kx^2 + bx + c.

In this case, the “k” will indicate whether the graph will be opening upwards to form a “u” shape or it opens downwards to form a “n” shape

When “k” is positive, the graph would open upwards and form a “u”.

If “k” is negative, the graph would open downwards and form a “n”.

Have a great day ahead!