Q45. - Algebra 2

Question

The shape of each arch supporting the Exchange House can be modeled by $h\left(x\right)=-0.025x^2+2x$, where h(x) represents the height of the arch and x represents the horizontal distance from one end of the base in meters.

 

According to this model, what is the maximum height of the arch?

Step-by-Step Solution

Answer

The maximum height of the arch is 40.

Step 1. Given Information.

Given that the shape of each arch supporting the Exchange House can be modeled by $h\left(x\right)=-0.025x^2+2x$, where $h\left(x\right)$ represents the height of the arch and x represents the horizontal distance from one end of the base in meters.

 

The equation of the axis of symmetry is x=40 and the coordinates of the vertex of the graph is $\left(40,40\right)$.

 

The maximum height of the arch is to be determined.

Step 2. Explanation .

Since x represents the distance from one end, the starting point is x=0.

Hence the vertex represents the highest point of the arch.

Here the vertex is at $\left(40,40\right)$

Hence the maximum height of the arch is 40.

Step 3. Conclusion .

The maximum height of the arch is 40.