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camicat

Member

Registered: 2020-02-27

Posts: 11

Algebra 2 Factoring Polynomials

Hello,
I (mostly) understand how to factor polynomials, but word questions always trip me up! Here is the current question that is confusing me:

Suppose a football is kicked from the ground and its height, h, in feet above the ground is given by h = -3.9t2 + 15.6t.

The time, t, represents the number of seconds after the ball is kicked. At what time does the football hit the ground?

Thanks in advance

Bob

Administrator

Registered: 2010-06-20

Posts: 10,803

Re: Algebra 2 Factoring Polynomials

hi camicat

Welcome to the forum.

This is the equation for motion under gravity for an object that starts on the ground and is projected upwards with a certain velocity.

You'll get a better idea of this if you draw a graph.  This link:

https://www.mathsisfun.com/data/function-grapher.php

will take you to the MIF graph plotter.  Enter the equation like this

-3.9x^2 + 15.6x

The plotter uses 'y' instead of 'h' and 'x' instead of 't'.

You'll also have to zoom out to see the highest point of the graph.

At t = 0 the ball is on the ground so h = 0.

When h is zero for the second time the ball is back on the ground.  So you need to solve

This should be easy for you to factorise because you already know that x = 0 is one solution. So factorise out an x

and the other value of x is the answer to the question.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

camicat

Member

Registered: 2020-02-27

Posts: 11

Re: Algebra 2 Factoring Polynomials

Hello Bob,

Thank you for your reply! I am still a bit confused, though. It has been a while since I have done basic algebra, so I feel that I may just be forgetting how to do this. Here is what I have done so far:

h = -3.9t^2 + 15.6t
0= -3.9t^2 + 15.6t
0 = 3.9 (-t^2 + 4t)
0 = -3.9t (t + 4)

I feel like I have not found the value that I am supposed to find, but I honestly don't even know what value I am trying to find. I am honestly just very confused and frustrated with myself for feeling like I have forgotten how to do a simple problem. I would appreciate any help you could give me with straightening out what I am doing.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,803

Re: Algebra 2 Factoring Polynomials

hi camicat

You're nearly there.  Tiny mistake in your last step:

0 = 3.9 (-t^2 + 4t)
0 = -3.9t (t + 4)

If you factorise -t out of the bracket then +4t becomes -4.  That's because -t x -4 = + 4t  not -t x +4

So the last line should be

0 = -3.9t (t - 4)

So either-3.9t = 0 (but you know this because t=0 was the time when the object started) or t-4 = 0

and that's the other time when the height is zero.

If you follow the link in my last post to the grapher you can put in y = -3.9x^2 + 15.6x ( have to use x and y not h and t) and you'll see the motion of the object as time passes crossing the x axis at t = 4.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob