## Compassionate one year ago A ball is shot from a cannon into the air with an upward velocity of 40 ft/sec. The equation that gives the height (h) of the ball at any time (t) is: h(t)= -16t2 + 40ft + 1.5. Find the maximum height attained by the ball.

1. Mehek14

$$\tt{x=\dfrac{-b}{2a}}$$

2. Compassionate

$\frac{ -b }{ 2a}$ $\frac{ -40 }{ -32 }$ Time = 8

3. SolomonZelman

4. SolomonZelman

$$h(t)= -16t^2 + 40t + 1.5$$ ?

5. SolomonZelman

the max height will be the vertex (because the parabola opens down, and that is because the leading coefficient is negative)

6. Compassionate

I need to find the maximum height. Yes, that's the equation. So my time is 8, right? To find my height, plug 8 in.

7. SolomonZelman

You don't need the height, if you are given that function you can find the vertex and that will be your maximum height.

8. Compassionate

To find max height, I need to first obtain the time it takes the ball to reach it, then plug in t.

9. Mehek14

how did you get time = 8? $$\tt{\dfrac{-40}{-32}=1.25}$$ not 8

10. Compassionate

I got 8 because my calculator is autistic and I am jut realizing this. -16(1.25)^2 + 40(1.25) + 1.5 -25 + 50 + 1.5 25 + 1.5 Height = 26.5

11. Mehek14

maximum height is 26.5 you get the time 1.25 and plug it in for t

12. Compassionate

Thanks! I got it :) `

13. Mehek14

when you use $$\tt{x=\dfrac{-b}{2a}}$$, you find the time then you plug the time in for the variable and yw :]

14. SolomonZelman

$$\large\color{black}{ \displaystyle h(t)=-16t^2-40t+1.5 }$$ $$\large\color{black}{ \displaystyle h(t)=-16(t^2+2.5t)+1.5 }$$ side caclulation: $$\large\color{black}{ \displaystyle 2.5\div2=1.25 }$$ $$\large\color{black}{ \displaystyle 1.25^2=1.5625 }$$ $$\large\color{black}{ \displaystyle h(t)=-16(t^2+2.5t+1.5625-1.5625)+1.5 }$$ $$\large\color{black}{ \displaystyle h(t)=-16(t^2+2.5t+1.5625)+(-16)(-1.5625)+1.5 }$$ $$\large\color{black}{ \displaystyle h(t)=-16(t+1.25)^2+25+1.5 }$$ $$\large\color{black}{ \displaystyle h(t)=-16(t+1.25)^2+26.5 }$$ So the height is 26.5 and it occurs at t=1.25.

15. SolomonZelman

(via completing the square)

16. Compassionate

I never learned how to complete squares :(

17. Compassionate

Okay, so can I shoot one more at you guys?

18. Mehek14

don't you learn completing the square in Alg 1?

19. SolomonZelman

I don't think there is a single particular order for learning different concepts in math.... I have seen people who asked how to find a slope in DE section.

20. SolomonZelman

Well, completing the square is something that you can probably browse and find a good resource quite fast:)