Question 130701


To find the x-intercept, plug in {{{y=0}}}



{{{y=-x^2+3x+18}}} Start with the given equation



{{{0=-x^2+3x+18}}} Plug in {{{y=0}}}



{{{0=-(x-6)(x+3)}}} Factor the right side 




Now set each factor equal to zero:

{{{x-6=0}}} or  {{{x+3=0}}} 


{{{x=6}}} or  {{{x=-3}}}    Now solve for x in each case



So our x-intercepts are 



(-3,0) and (6,0) 



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To find the y-intercept, plug in {{{x=0}}}


{{{y=-x^2+3x+18}}} Start with the given equation



{{{y=-(0)^2+3(0)+18}}} Plug in {{{x=0}}}



{{{y=0+3*0+18}}} Raise 0 to the 2nd power to get 0



{{{y=0+0+18}}} Multiply 3 and 0 to get 0



{{{y=0+18}}} Add 0 and 0 to get 0



{{{y=18}}} Add 0 and 18 to get 18



So the y-intercept is (0,18)





Notice if we graph {{{y=-x^2+3x+18}}}  we can  visually verify our answer.



{{{ graph(500,500,-10,10,-10,20,0, -x^2+3x+18) }}}