Question

look closely at the following \two wrongs and a right\. determine which graph is
ight\. in your post, fully explain your answer. be sure to use the term vertex in your response. parabola with vertex (2, -3) parabola with vertex (2, -3) parabola with vertex (2, -3) two wrongs

Explanation:

Step1: Recall vertex definition

The vertex of a parabola is the point where the parabola changes direction. For a parabola with vertex $(h,k)$, the $x -$coordinate of the vertex is $h$ and the $y -$coordinate is $k$. Here $h = 2$ and $k=-3$.

Step2: Check x - coordinate on graphs

Look for the $x -$value of the vertex on the x - axis of each graph. The correct graph should have the vertex's x - value at $x = 2$.

Step3: Check y - coordinate on graphs

Look for the $y -$value of the vertex on the y - axis of each graph. The correct graph should have the vertex's y - value at $y=-3$.

Step4: Analyze graphs

The first graph has its lowest point (vertex for an upward - opening parabola) at approximately $(2,3)$ which is wrong. The second graph has its vertex at approximately $(- 2,-3)$ which is wrong. The correct graph is the one where the vertex is at the point with $x = 2$ and $y=-3$ (assuming the third graph has the correct vertex location based on the problem's setup).

Answer:

The graph with the vertex actually located at the point $(2,-3)$ on the coordinate - plane is the right one.