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A ball is thrown vertically upward with an initial velocity of 80 feet per second. The distance $s$ (in feet) of the ball from the ground after $t$ seconds is $s(t)=80 t-16 t^{2}$

a.5 secondsb. between 2 and 3 seconds

Algebra

Chapter 4

Linear and Quadratic Functions

Section 5

Inequalities Involving Quadratic Functions

Equations and Inequalities

Linear Functions

Quadratic Functions

Solve Linear Inequalities

Graph Linear Functions

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this problem is a question about a ball that has been thrown into the air and is being affected by gravity and bringing it back to the earth. This equation is representing that ball being thrown in. The air is been thrown at 80 feet per second and this is acceleration due to gravity being brought back down of negative 16. And so what this question is asking us is two parts part a is asking us win. When is a time question? When will the ball land back on the ground? And that will happen when the Prabal Owen s of t will equal zero when the graph equals zero. And we want to know when this occurs. Well, it equals zero when the time when the y value is zero. That's what this is telling me when the Y value is equal to zero. What is the time so we can use a graphing utility to help us out. So here I have the equation. S f T equals 80 T minus 16 T square. And here's the problem. Here is where it starts at 00 It's thrown into the air and it reaches a peak at 2.5 seconds of 100 feet and gradually falls back to the ground and it crosses. The X axis had five. So here is when it lands on the ground. So how long did it take to land back on the ground? Five seconds. So the answer to a is X equals five. And let's just go ahead, make it correct. Five seconds. Question be asks us the question For what time? How long is the graph above? For what time? Tea is the ball more than 96 feet above the ground. For what time? How long, Basically, is it above 96 feet? So what that means is we're asking Win His sf t Part B is asking Windows S of t greater than 96. That's what the question is asking us. And so again we can use the graphing utility to help us out. So here I have the line of y equals 96 feet and it's a vertical line horizontal line, and I want to know how long. What time interval is it above? It's above 96 feet between two and three seconds. So that's exactly what I'm going to say between two and three seconds to is less than X, which is less than three, which means between to and three seconds.

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