Question 1124230
Below is the table: 

{{{x}}}- {seconds after the ball is thrown)
{{{ y}}}-(ball's height, infeet, above the ground)



{{{x}}}                              |{{{y}}}
{{{1	}}}                                                          {{{339}}}
{{{3}}}	                                                             {{{321}}}
{{{4	}}}                                                          {{{ 264}}}

Find the quadratic function {{{y= ax^2 + bx + c}}} whose graph passes through the given points.

{{{y= ax^2 + bx + c}}}...plug in {{{x=1}}},{{{y=339}}}

{{{339= a*1^2 + b*1 + c}}}
{{{339= a + b + c}}}........eq.1


{{{y= ax^2 + bx + c}}}...plug in {{{x=3}}},{{{y=321}}}

{{{321= a*3^2 + b*3 + c}}}
{{{321= 9a + 3b + c}}}........eq.2


{{{y= ax^2 + bx + c}}}...plug in {{{x=4}}},{{{y=264}}}

{{{264= a*4^2 + b*4 + c}}}
{{{264= 16a + 4b + c}}}........eq.3

------------------------------solve the system

{{{339= a + b + c}}}........eq.1
{{{321= 9a + 3b + c}}}........eq.2
-----------------------------------------subtract eq2 from eq1

{{{339-321= a-9a + b-3b + c-c}}}

{{{18= -8a -2b }}}....solve for {{{a}}}

{{{8a=  -2b-18 }}}

{{{a=  -2b/8-18/8 }}}

{{{a=  -b/4-9/4 }}}...............eq.1a

go to

{{{264= 16a + 4b + c}}}........eq.3
{{{321= 9a + 3b + c}}}........eq.2
-----------------------------------------------subtract eq.2 rom eq.3

{{{264-321= 16a-9a + 4b-3b + c-c}}}

{{{-57= 7a + b}}}

{{{-57-b= 7a }}}

{{{a=-57/7-b/7 }}}...............eq.1b


from eq.1a and eq.1b we have:

{{{ -b/4-9/4= -57/7-b/7}}}............solve for {{{b}}}

{{{ (-b-9)/4= (-57-b)/7}}}

{{{7(-b-9)= 4(-57-b)}}}

{{{-7b-63= -228-4b}}}

{{{228-63= 7b-4b}}}

{{{165= 3b}}}

{{{ b=165/3}}}

{{{highlight( b= 55)}}}

go back to {{{a=  -b/4-9/4 }}}...............eq.1a, substitute {{{b}}}

{{{a=  -(55)/4-9/4 }}}

{{{a=  -(55+9)/4 }}}

{{{a=  -64/4 }}}

{{{highlight(a=  -16) }}}


go to {{{339= a + b + c}}}........eq.1, substitute {{{a}}} and {{{b}}}

{{{339= -16 +55 + c}}}

{{{339= 39+ c}}}

{{{c=339-39}}}

{{{highlight(c=300)}}}

then, your equation is:

{{{highlight(y= -16x^2 +55x + 300 )}}}