SOLUTION: Find the x and y intercepts for the given equation {{{y=-x^2+3x+18}}}

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Question 130701: Find the x and y intercepts for the given equation


y=-x%5E2%2B3x%2B18


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


y=-x%5E2%2B3x%2B18 Start with the given equation


0=-x%5E2%2B3x%2B18 Plug in y=0


0=-%28x-6%29%28x%2B3%29 Factor the right side



Now set each factor equal to zero:
x-6=0 or x%2B3=0

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


So our x-intercepts are


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





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

y=-x%5E2%2B3x%2B18 Start with the given equation


y=-%280%29%5E2%2B3%280%29%2B18 Plug in x=0


y=0%2B3%2A0%2B18 Raise 0 to the 2nd power to get 0


y=0%2B0%2B18 Multiply 3 and 0 to get 0


y=0%2B18 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%5E2%2B3x%2B18 we can visually verify our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C20%2C0%2C+-x%5E2%2B3x%2B18%29+