High School

The height, in feet, of an object [tex]\( x \)[/tex] seconds after it is thrown straight up in the air can be modeled by the function [tex]\( h(x) = -16x^2 + 20x + 5 \)[/tex]. Based on the model, which of the following statements best interprets the equation [tex]\( h(1.4) = 1.64 \)[/tex]?

A. The height of the object 1.4 seconds after being thrown straight up in the air is 1.64 feet.
B. The height of the object 1.64 seconds after being thrown straight up in the air is 1.4 feet.

Answer :

We are given the height function

[tex]$$
h(x) = -16x^2 + 20x + 5,
$$[/tex]

where [tex]$x$[/tex] represents the time in seconds after the object is thrown, and [tex]$h(x)$[/tex] gives the height in feet.

To determine the height of the object at 1.4 seconds, we substitute [tex]$x = 1.4$[/tex] into the function:

[tex]$$
h(1.4) = -16(1.4)^2 + 20(1.4) + 5.
$$[/tex]

Following the order of operations:

1. First, calculate [tex]$(1.4)^2$[/tex].
2. Multiply the result by [tex]$-16$[/tex].
3. Then, compute [tex]$20 \times 1.4$[/tex].
4. Finally, add these results to the constant term [tex]$5$[/tex].

After performing these calculations, we find that

[tex]$$
h(1.4) \approx 1.64.
$$[/tex]

This means that 1.4 seconds after the object is thrown, its height is approximately 1.64 feet.

Thus, the correct interpretation is:

A. The height of the object 1.4 seconds after being thrown straight up in the air is 1.64 feet.