Algebra 2 problem

Question

Y= -8t^2 + 32t + 96

How long is the pebble in the air in seconds?

With steps please and thank you.

Answer 1

This is a quadratic function, which means it will have two solutions, or x-intercepts. This particular function is also easy to factor:

1. Take out the GCF, -8: y= -8(t²-4t-12).
2. Factor the quadratic in the parenthesis using the ac method: y= -8(t-6)(t+2) -->If you don't know the ac method, try Googling "ac method of factoring".
3. Set this equal to zero to find the possible solutions: 0 = -8(t-6)(t+2)
4. If (t-6)=0, t=6.
5. If (t+2)=0, t=-2.
6. We don't use negative time, so we'll only account for the time from t=0 to the solution t=6. Therefore, the pebble is in the air for 6 seconds.
7. Alternatively, you could graph the function, look at the x-intercepts, and see that the graph crosses the x-axis at x=-2 and x=6. Again, we don't think about time as something that can be negative, so from 0 seconds when the pebble is thrown to 6 seconds, when it lands on the ground, is the time it's in the air.

I hope this helps, and have fun mathing!

Liz Z.