6. A ball is hit into the air. Its height, $h$, in metres after $t$ seconds can be modeled by $h=-5 t^{2}+40 t+1$
a) What is the maximum height of the ball? [2]
b) How long does the ball take to reach this height? [2]
c) What is the initial height of the ball? [1]

Answer

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Answer

\boxed{1}

Steps

Step 1 ：$-5t^2+40t+1=-5(t^2-8t)+1$

Step 2 ：$-5(t^2-8t)+1=-5(t^2-8t+16-16)+1$

Step 3 ：$-5(t^2-8t+16-16)+1=-5([t-4]^2-16)+1$

Step 4 ：$-5(t-4)^2+81$

Step 5 ：\boxed{81}

Step 6 ：$t=4$

Step 7 ：$h(0)=-5(0)^2+40(0)+1$

Step 8 ：\boxed{1}