Question

The graph of f (x) = -0.01x² + x can be used to model the height in feet of a

curved arch support for a bridge, where the x-axis represents the water level and x
represents the distance in feet from where the arch support enters the water. Find the height of the highest point of the bridge.

Answer 1

Answer: 25 feet.

Explanation:

The height of the highest point is the y-coordinate of the vertex parabola. You can follow these steps:

1, Find the x-coordinate of the vertex with the following formula:

`x=(-b)/(2a)`

In this case, you can identify that:

`a= -0.01\\\\b=1`

2. Knowing these values you can substitute them into the formula and then evaluate:

`x=(-1)/((2)(-0.01))\\\\x=50`

3. Rewrite the function as:

`y= -0.01x^2 + x`

4. Substitute the value of "x" into the function and evaluate:

`y= -0.01(50)^2 + 50\\\\y=25`

Therefore, the height of the highest point of the bridge is 25 feet.