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21 votes
21 votes
A bridge is supported by three arches. The function that describes the arches is

h(x) = -0.2x² + 3.0x, where h(x) is the height, in metres, of the arch above the ground at any distance, x, in metres,
from one end of the bridge. How tall is each arch?

User Warren Nocos
by
2.7k points

1 Answer

12 votes
12 votes

Answer:

11.25 meters

Explanation:

To find the maximum height of a parabola, we use the quadratic equation

x = -b/2a.

Given the equation (It's in Standard Form, Ax^2 + By = C)

So it's -3 / (2 * -0.2) which is equal to 7.5.

Now that we know the value of x, we plug in x into the equation.

-0.2(7.5^2) + 3.0(7.5) = height.

-0.2(56.25) + 22.5 = height.

-11.25 + 22.5 = height.

h(x) = 11.25

User Lee Hambley
by
2.7k points