Maximum Height in the Real World (3.14.4)

Question 1

• Standard form of a parabola:
f(x) = ax^2 + bx + c.

• Vertex of a parabola:
(h, k), where and k = f (h).

• Standard form for parabola showing vertex:
f(x) = a (x – h)^2 + k.

Answer 1

• Standard form of a parabola:
f(x) = ax^2 + bx + c.

• Vertex of a parabola:
(h, k), where and k = f (h).

• Standard form for parabola showing vertex:
f(x) = a (x – h)^2 + k.

Question 2

In this example, your x-axis represents the distance in feet that the bridge spans.

The graph is set so that x = 0 where the bridge’s curve is at its highest; i.e., at the vertex.

So, h = 0.

Solve for k, which turns out to be 27 feet.

Now you want to find the height of the span 10 feet on either side of center.

This means x = 10.

Substitute 10 into the function for x and solve for the y, or
height.

That height is 22.312 feet.

Now you want to find the location of a specific height of the span of the bridge.

Set the height to 8 feet; i.e., h (x) = 8. That means that the
function, h (x), equals 8. Now solve for x.

The edge of the bridge is 8 feet above its base on either side at 20.13 feet from the height of the arch.

Answer 2

In this example, your x-axis represents the distance in feet that the bridge spans.

The graph is set so that x = 0 where the bridge’s curve is at its highest; i.e., at the vertex.

So, h = 0.

Solve for k, which turns out to be 27 feet.

Now you want to find the height of the span 10 feet on either side of center.

This means x = 10.

Substitute 10 into the function for x and solve for the y, or
height.

That height is 22.312 feet.

Now you want to find the location of a specific height of the span of the bridge.

Set the height to 8 feet; i.e., h (x) = 8. That means that the
function, h (x), equals 8. Now solve for x.

The edge of the bridge is 8 feet above its base on either side at 20.13 feet from the height of the arch.