Question

An arch is in the form of a parabola given by the function h = -0.06d^2 + 120, where the origin is at ground level, d meters is the horizontal distance and h is the height of the arch in meters.
Graph this function on your graphing calculator then complete the following statements.
The height of the arch is: ------- m
The width to the nearest meter, at the base of the arch is ------ m

Answer 1

Answer:

See attachment for graph

The height of the arch is: 120 m

The width to the nearest meter, at the base of the arch is 22 m

Step-by-step explanation:

Given

$h = -0.06d^2 + 120$

Solving (a): The graph

See attachment for graph

Variable h is plotted on the vertical axis while variable d is plotted on the horizontal axis.

Solving (b): The height

The curve of $h = -0.06d^2 + 120$ opens downward. So, the maximum point on the vertical axis represents the height of the arch,

Hence:

$height = 120$

Solving (c): The width

The curve touches the horizontal axis at two different points.

$x_1 = -11$

$x_2 = 11$

The absolute difference of both points represents the width.

So:

$Width = |x_2 - x_1|$

$Width = |11 - -11|$

$Width = |11 +11|$

$Width = |22|$

Hence:

$Width = 22$