SOLUTION: Hi can someone please help me answer this question? thanks so much Describe three ways to determine the zeros of the quadratic function f(x)=-3x^2+27x-42. Solve for the zeros fo

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hi can someone please help me answer this question? thanks so much Describe three ways to determine the zeros of the quadratic function f(x)=-3x^2+27x-42. Solve for the zeros fo      Log On


   

Question 1090512: Hi can someone please help me answer this question? thanks so much
Describe three ways to determine the zeros of the quadratic function f(x)=-3x^2+27x-42. Solve for the zeros for each method.
Found 2 solutions by Fombitz, Boreal:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Graphically,
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Factoring,
f%28x%29=-3x%5E2%2B27x-42
f%28x%29=-3%28x%5E2-9x%2B14%29
f%28x%29=-3%28x-2%29%28x-7%29
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Completing the square,
f%28x%29=-3%28x%5E2-9x%29-42
f%28x%29=-3%28x%5E2-9x%2B%289%2F2%29%5E2%29-42%2B3%289%2F2%29%5E2
f%28x%29=-3%28x-9%2F2%29%5E2-42%2B243%2F4
f%28x%29=-3%28x-9%2F2%29%5E2-168%2F4%2B243%2F4
f%28x%29=-3%28x-9%2F2%29%5E2%2B75%2F4
So,
-3%28x-9%2F2%29%5E2%2B75%2F4=0
3%28x-9%2F2%29%5E2=75%2F4
%28x-9%2F2%29%5E2=25%2F4
x-9%2F2=0+%2B-+5%2F2
x=9%2F2%2B-5%2F2
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x=14%2F2=7
x=4%2F2=2


Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=-3x^2+27x-42.
factor -3(x^2-9x+14)=-3(x-7)(x-2)=0, and x=7, 2
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complete the square after first changing all signs to 3x^2-27x+42=0 and move the constant so that 3x^2-27x=-42
divide the left side by 3 to get 3(x^2-9x) and complete the square by taking half of -9 and squaring it to get 20.25; X^2-9X+20.25=-42+3(20.25)
add 60.75 to the right because of the 3
now it is 3(x-4.5)^2=18.75
Divide by 3
(x-4.5)^2=6.25
take the square root.
x-4.5=+/- 2.5
x=7, 2
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graph it
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-3x%5E2%2B27x-42%29