Question

question
determine the vertex of the parabola whose graph is given below.
give your answer as an ordered pair $(h,k)$. for example, if you found the vertex was at $(1,2)$, you would enter $(1,2)$.
provide your answer below:

Explanation:

Step1: Understand the vertex of a parabola

The vertex of a parabola is the point where the parabola changes direction. It is either the minimum (for a parabola opening upwards) or the maximum (for a parabola opening downwards) point on the graph.

Step2: Locate the vertex on the graph

Looking at the given graph of the parabola (which opens upwards), we observe the lowest point. By checking the coordinates on the \(x - y\) plane:

• The \(x\) - coordinate (\(h\)) of the vertex is found by looking at the horizontal position. Each grid - line represents \(1\) unit. The vertex is \(4.5\) units to the left of the \(y\) - axis (since \(x=- 4.5\)).
• The \(y\) - coordinate (\(k\)) of the vertex is found by looking at the vertical position. The vertex is \(1.5\) units below the \(x\) - axis (since \(y =-1.5\)).

Answer:

\((-4.5,-1.5)\)