Question 1003837
write an equation of the parabola that passes through the point (3,-30) and has x-intercepts -2 and 18.
<pre>
{{{x=-2}}}, {{{x=18}}}

{{{x+2=0}}},  {{{x-18=0}}}

{{{y = a(x+2)(x-18)}}}

{{{y = a(x^2-16x-36)}}}

Substitute (x,y) = (3,-30)

{{{-30 = a(3^2-16*3-36)}}}

{{{-30 = a(9-48-36)}}}

{{{-30 = a(-75)}}}

{{{(-30)/(-75)=a}}}

{{{2/5=a}}}

So the equation 

{{{y = a(x^2-16x-36)}}}

becomes:

{{{y = expr(2/5)(x^2-16x-36)}}}

{{{y = expr(2/5)x^2-expr(32/5)x-expr(72/5))}}}

Edwin</pre>

{{{drawing(9600/23,800,-4,20, -42,4,

circle(3,-30,0.15),circle(3,-30,0.13),circle(3,-30,0.11),circle(3,-30,0.09),circle(3,-30,0.07),circle(3,-30,0.05),circle(3,-30,0.03),circle(3,-30,0.01),

locate(3.2,-29.5,"(3,-30)"),

graph(9600/23,800,-4,20, -42,4, (2/5)(x^2-16x-36)) )}}}

Edwin</pre>