Question

When a person weighing 145 pounds dives into a pool their path can be modeled by the equation y=2x^2-16x+14 where y is the height/depth of the person's head x seconds after leaving the diving platform. a. Draw a detailed sketch of the scenario that is modeled by the given formula.Graph such that the x-values go from 0 to 10 and y-values go from -20 to 20.c. How deep does the pool need to be for the person to avoid hitting their head?d. How long before the diver resurfaces?

Answer 1

Answer and Explanation:

Given the below equation;

`y=2x^2-16x+14`

where y = the height/depth of the person's head

x = seconds after leaving the diving platform.

a) We're told that the values of x should go from 0 to 10.

To be able to plot the graph, let's choose different values of x and find the corresponding values of y.

When x = 0;

`\begin{gathered} y=2(0)^2-16(0)+14 \\ y=14 \end{gathered}`

When x = 2;

`\begin{gathered} y=2(2)^2-16(2)+14 \\ y=8-32+14 \\ y=-10 \end{gathered}`

When x = 6;

`\begin{gathered} y=2(6)^2-16(6)+14 \\ y=72-96+14 \\ y=-10 \end{gathered}`

When x = 8;

`\begin{gathered} y=2(8)^2-16(8)+14 \\ y=128-128+14 \\ y=14 \end{gathered}`

When x = 10;

`\begin{gathered} y=2(10)^2-16(10)+14 \\ y=200-160+14 \\ y=54 \end{gathered}`

See below the graph of the given equation;

c) We're told from the que