which graph represents a quadratic function with a vertex at (0, 0)?

Explanation:

Step1: Recall quadratic - function vertex form

The vertex - form of a quadratic function is $y = a(x - h)^2+k$, where $(h,k)$ is the vertex. When the vertex is $(0,0)$, the function is $y = ax^2$. The graph of $y = ax^2$ is a parabola with its vertex at the origin $(0,0)$. A parabola $y = ax^2$ has a U - shape. If $a>0$, it opens upwards; if $a < 0$, it opens downwards.

Step2: Analyze the given graphs

The graph of a quadratic function $y=ax^2$ with $a>0$ has a vertex at $(0,0)$ and opens upwards. The first graph shown has a U - shape and its lowest point (vertex) is at the origin $(0,0)$.

Answer:

The first graph (the one with a U - shape and vertex at the origin)