We know two points: (0, 6) (the ball was 6 feet high at time 0 when it was thrown), and (2.5, 106) (that's the time and max height they give us). We can plug both of those points into the function to figure out the constants. Start with (0, 6):

6 =

*c*- (*d*- 0)^{2}6 =

*c*-*d*^{2}106 =

*c*- (*d*- 4(2.5))^{2}106 = c - (

*d*- 10)^{2}FOIL it out:

106 =

*c*- (*d*^{2 }- 20*d*+ 100)Distribute the negative:

106 =

*c*-*d*^{2 }+ 20*d*- 100*c*-

*d*

^{2 }= 6 (I bet you were wondering why I made it red...), so substitute that into the 2nd equation

106 = 6 + 20

*d*- 100100 = 20

*d*- 100200 = 20

*d*10 =

*d**c*-

*d*

^{2 }= 6 one more time to figure out

*c*:

*c*- 10

^{2 }= 6

*c*- 100 = 6

*c*= 106

*t*= 1:

*h*(

*t*) =

*c*- (

*d*- 4

*t*)

^{2}

*h*(1) = 106 - (10 - 4)

^{2}

*h*(1) = 106 - 6

^{2}

*h*(1) = 106 - 36

*h*(1) = 70

Note that there's a shortcut here, but it's very tricky to see it. The key is to recognize that this equation will hit its maximum (remember, the maximum was at

*t*= 2.5) when (

*d*- 4

*t*)

^{2}= 0. From there, you know immediately that

*c*= 106, and

*d*= 10. Want more clarification on this shortcut? Ask in the comments!

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