Question

What is the value of a in this equation?

Answer 1

Substituting into vertex form, we can write the equation of the parabola as

`y=a(x-0)^(2)+9\\\\y=ax^(2)+9`

To find the value of a, we can substitute in the coordinates of another point the graph passes through, such as (3,0).

`0=a(3)^(2)+9\\\\0=9a+9\\\\-9=9a\\\\a=\boxed{-1}`