The height of a toy rocket in feet is molded by h=-8^2 + 48x. where x is the time in seconds after it is launched. how long is the rocket in the air

Answer 1

Molly,

Since this is a quadratic function, and x represents time, we are looking to see where this function would cross the x-axis if we were to graph it. This is where our our height is zero. There are two times when our height is zero (where the function crosses the x-axis), when the rocket takes off and when it lands. We are looking for the zeros of this function. Again, we are looking for when our height is zero, so the first thing we can do is plug in zero for h:

-8x^2 + 48x = 0

Now we need to solve for x. There are many ways to do this. One way is by completing the square:

1. Divide each term by -8 to make the coefficient of the quadratic term 1
2. x^2 - 6x = 0
3. Complete the square using (b/2)^2, where b in this case is -6
4. (-6/2)^2 = (-3)^2 = 9
5. We are adding 9 to both sides to make a perfect square trinomial on the left side: x^2 - 6x + 9 = 9
6. Rewrite the left side as a binomial squared
7. (x - 3)^2 = 9
8. Take the inverse operation of the squared (square root) to get rid of the exponent, must do to both sides
9. sqrt(x - 3)^2 = sqrt(9)
10. sqrt(9) can equal a positive 3 or a negative 3, so you will be left with two equations
11. x - 3 = 3 or x - 3 = -3
12. Solve for x:
13. x - 3 = 3 add 3 to both sides ---> x = 6
14. x - 3 = -3 add 3 to both sides ---> x = 0

Since x represents time, x = 0 represents our starting time, so that means x = 6 when the rocket lands.

Therefore, the rocket is in the air for 6 seconds.

Hope this helps

Answer 2

Molly, can you clarify the model equation: is it:

-(8)^2 or (-8)^2 . The reason why I am confused is that if it is the former, this implies that you are launching the rocket from some position 64 feet below some level. Am I possibly miss reading the equation completely

Answer 3

Hi Molly.

if h= -8x^2+48x is the flight of the rocket, then the time the rocket is in the air will be when h = 0.

0=-8x^2+48x factor out -8x from both terms

0=-8x(x-6) set both terms equal to zero to determine the x intercepts

-8x=0 divide both sides by -8, and you get x=0. this is the time that the rocket is launched.

x-6=0 add 6 to both sides and you get x=6. this is the time that the rocket hits the ground at the end of its flight. X=6

Hope this helps.

michael.russell.10