1. Vector Question

For any vectors v and w, consider the following function of scalar t:
q(t)=(v+t w) dot (v+ t w).
(1) Explain why q(t) is greater than or equal to 0 for all real t.
(2) Expand q(t) as quadratic polynomial in t using the dot product properties.

2. Originally Posted by vvc531
For any vectors v and w, consider the following function of scalar t:
q(t)=(v+t w) dot (v+ t w).
(1) Explain why q(t) is greater than or equal to 0 for all real t.
(2) Expand q(t) as quadratic polynomial in t using the dot product properties.
Should this look like this?

$q(t)=\cdot$