a toy cannon ball is launched from a cannon on top of a platform . The equation h(t)=-5t^2+20t+4 gives the height h, in meters, of the bell t seconds after it is launched. what equation can be used to tell whether the ball reaches a height of 12 m?

Answer 1

To determine whether the ball reaches a height of 12 meters, we need to set up the equation and solve for t.

Given that h(t) = -5t^2 + 20t + 4, we can set it equal to 12:

-5t^2 + 20t + 4 = 12

Rearranging the equation:

-5t^2 + 20t + 4 - 12 = 0

-5t^2 + 20t - 8 = 0

Now we have a quadratic equation. To solve for t, we can either factor it or use the quadratic formula. To factor it, we can start by factoring out a common factor of -1:

-t^2 + 4t + 8 = 0

Now, we can try factoring by grouping. Splitting the middle term:

(-t^2 + 8t) + (4t + 8) = 0

Factoring out a common factor in each group:

-t(t - 8) + 4(t + 2) = 0

Now we can factor out the common factors:

-t(t - 8) + 4(t + 2) = 0

-t(t - 8) - 4(t - 2) = 0

Now, we have two factors:

t - 8 = 0 or t + 2 = 0

Solving for t:

t = 8 or t = -2

Therefore, the ball reaches a height of 12m either at 8 seconds or -2 seconds. However, since time cannot be negative, the ball reaches a height of 12m at t = 8 seconds.