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 ： $- 5 t^{2} + 40 t + 1 = - 5 (t^{2} - 8 t) + 1$

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

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

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}