Question 993370
a) What does {{{x}}} and {{{y}}} represent in this situation?

{{{y}}}  represent height (dependent variable,depends on how {{{x}}} changes ) 
{{{x}}} represent the path (dependent variable,it is a variable that stands alone and isn't changed by the other variables you are trying to measure )

b)
If it is known that the point ({{{10}}},{{{15}}}) lies on the path given by the equation {{{y=ax^2+bx+c}}}, use algebra and all the information given in a) and b) to show that: 
{{{a = -2/75}}}, {{{b = 47/30}}} and {{{c = 2}}}

if the point ({{{x}}},{{{y}}})=({{{10}}},{{{15}}}),  we have

{{{y=ax^2+bx+c}}} 

{{{15=100a+10b+c}}} ..............eq.1

 if {{{a = -2/75}}}, {{{b = 47/30}}} and {{{c = 2}}}, we have equation like this:

{{{y=-(2/75)x^2+(47/30)x+2 }}}...now,show that {{{y=15}}} when {{{x=10}}}


{{{y= -(2/75)10^2+(47/30)10+2 }}}

{{{y= -(2/75)100+(47/30)10+2 }}}

{{{y= -(2/15)20+(47/3)+2 }}}

{{{y= -(40/15)+(47/3)+2 }}}

{{{y= -(40/15)+((47*5)/15)+(2*15)/15 }}}

{{{y= (-40+235+30)/15}}}
 
{{{y= 225/15}}}
 
{{{y= 15 }}}


c)

Hence find the height {{{y}}}  of the javelin after traveling {{{x=20m}}} horizontally

{{{y= -(2/75)x^2+(47/30)x+2}}}
 
{{{y= -(2/75)20^2+(47/30)20+2 }}}

{{{y= -(2/75)400+(47*20)/30+2}}}

{{{y= -(800/75)+(940)/30+2}}}

{{{y= -(160/15)+(470/15)+30/15}}}

{{{y= (470-160+30)/15)}}}

{{{y= (500-160)/15)}}}

{{{y= 340/15)}}}

{{{y=22.66666666666667}}}

{{{y=22.7}}}


{{{drawing( 600, 600, -30, 50, -30, 50, 

circle(10,15,.2),circle(20,22.7,.2),
locate(10,15,p(10,15)),locate(20,22.7,p(20,22.7)),
 graph( 600, 600, -30, 50, -30, 50, -(2/75)x^2+(47/30)x+2 )) }}}