While using your Samsung Galaxy S7 you feel to battery start to heat up and thro

Question

While using your Samsung Galaxy S7 you feel to battery start to heat up and throw it in the air for safety. The height of the S7 can be modeled by the function: h(t) = 20t - 16t^2, t measured in seconds. (a) Rewrite the function in standard form by completing the square. (b) Find the maximum height of the phone. Construct a quadratic equation in standard form whose solution set is {2 + Squareroot 3, 2 - Squareroot 3}. Check that your equation has the correct solutions by. Bonus: A math teacher is going to draw a large rectangle on the board. They only have enough chalk left to draw for 100 inches. What is the maximum area that can be formed?

Explanation / Answer

h(t) = 20t -16t^2

a) h(t) = 20t -16t^2 = -( 16t^2 - 20t )

= - 4(4t^2 -5t) = -4( 4t^2 - 5t +25/4 - 25/4 )

h(t) = -4(2t -5/2)^2 + 25

b) maximum height occurs at : t = -b/2a = -(20/2*-16) = 20/32 = 10/16 = 5/8 sec = 0.625 sec

h(0.625) = 20*0.625 - 16(0.625)^2 = 6.25

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