# SOLUTION: A rocket is fired upward from the ground with an initial velocity of 80 feet per second. The polynomial 80x-16^2 describes the height of the rocket, in feet, after x seconds. a) F

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Question 5799: A rocket is fired upward from the ground with an initial velocity of 80 feet per second. The polynomial 80x-16^2 describes the height of the rocket, in feet, after x seconds.
a) Find the rocket's height after 4 seconds
b) Factor the polynomial
c) Use the factored form of the polynomial in part (b) to find the rocket's height after 4 seconds. Do you get the same answer as you did in part (a)?

You can put this solution on YOUR website!
You surely meant , right?
For height at 4 seconds, use "4" instead of "x":
Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: Graphical form: simplifies to Text form: 80*4-16*4^2 simplifies to 64Cartoon (animation) form: For tutors: `simplify_cartoon( 80*4-16*4^2 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Multiplied numerator integers
It becomes .

Look at .
Replace constants in factor: , with
It becomes .

Look at .
Replace constants in expression: , with
It becomes .
Result:

### Universal Simplifier and Solver

Done!

so, 64 is the height at 4 seconds.
To factor, I use my quadratic solver:
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=6400 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0, 5. Here's your graph:

factoring is -16x*(x-5).
If you again use 4 instead of x:
Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: Graphical form: simplifies to Text form: -16*4*(4-5) simplifies to 64Cartoon (animation) form: For tutors: `simplify_cartoon( -16*4*(4-5) )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Multiplied numerator integers
It becomes .

Look at .