The graph shows the average monthly high temperature in Newark NJ for months from April to September. If a quadratic model is fit to the graphed data set estimate the coordinates of the vertex.

Question

The graph shows the average monthly high temperature in Newark NJ for months from April to September. If a quadratic model  is fit to the graphed data set estimate the coordinates of the vertex.

Quizplus · Accepted Answer

The vertex of a quadratic function of the form f(x) = ax^2 + bx + c is located at (-b/2a, f(-b/2a)). In this case, we can see that the quadratic function has a negative leading coefficient, so it opens downwards and has a maximum at the vertex. We can estimate the vertex by finding the midpoint of the two x-intercepts on either side of the vertex. From the graph, it appears that the x-intercepts are at approximately x = 3 and x = 9, so the midpoint is x = 6. The corresponding y-value on the graph is approximately 82 degrees, so the vertex is estimated to be at (6, 82). Using the formula for the vertex, we obtain x = -b/2a = -(-16)/(2*(-0.4)) = 20 and f(20) = -0.4(20)^2 + 16(20) - 78 = 82, confirming that the estimated vertex is accurate. Thus, the answer is B.

The Graph Shows the Average Monthly High Temperature in Newark