Question

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

Explanation:

To determine which graph represents a quadratic function with a vertex at \((0, 0)\), we analyze the key features of a quadratic function's graph (a parabola) and the given options:

Step 1: Recall the vertex form of a quadratic function

A quadratic function with vertex \((h, k)\) is \( y = a(x - h)^2 + k \). For a vertex at \((0, 0)\), this simplifies to \( y = ax^2 \), where \( a
eq 0 \). The graph of \( y = ax^2 \) is a parabola with its vertex (minimum or maximum point) at the origin \((0, 0)\) and symmetric about the \( y \)-axis.

Step 2: Analyze the given graphs

• The first graph shown has its vertex at \((0, 1)\) (not \((0, 0)\)), so it does not satisfy the condition.
• The second graph (partially visible) likely has its vertex at \((0, 0)\) (since it appears to touch the origin and be symmetric about the \( y \)-axis).

Step 3: Confirm the vertex location

A vertex at \((0, 0)\) means the parabola must pass through the origin \((0, 0)\) and have its minimum/maximum point there. The second graph (with vertex at \((0, 0)\)) matches this description.

Answer:

The graph with vertex at \((0, 0)\) (the second graph, likely representing \( y = ax^2 \) with vertex at the origin).