The equation \( y = a(x + 3)^2 \) represents a quadratic function. This is evident because it can be expressed in the standard form of a quadratic equation, which is typically \( y = ax^2 + bx + c \).
In this particular case, the equation is in the vertex form of a quadratic, which is given by:
\[ y = a(x - h)^2 + k \]
where \( (h, k) \) is the vertex of the parabola.
Here, \( h \) is \(-3\) (since \( x + 3 \) can be rewritten as \( x - (-3) \)), and \( k \) is implicitly 0, meaning the vertex is at the point \((-3, 0)\). The value of \( a \) determines the direction and width of the parabola: if \( a > 0 \), the parabola opens upward, and if \( a < 0 \), it opens downward. The larger the absolute value of \( a \), the narrower the parabola.
In summary, \( y = a(x + 3)^2 \) is a quadratic function in vertex form, with its vertex at the point \((-3, 0)\).