1. Use the given information to determine the equation of each quadratic relation in vertex form, $y=a(x-h)^{2}+k$. a) $a=2$, vertex at $(0,3)$

Step 1 ：Use the given information to determine the equation of each quadratic relation in vertex form, $y=a(x-h)^{2}+k$.

Step 2 ：a) $a=2$, vertex at $(0,3)$

Step 3 ：We are given the value of $a$ and the vertex coordinates $(h, k)$. We can plug these values into the vertex form equation to find the equation of the quadratic relation.

Step 4 ：Final Answer: The equation of the quadratic relation in vertex form is $y = 2(x-0)^{2} + 3$, which simplifies to \(\boxed{y = 2x^{2} + 3}\).