i don't understand what you advise by utilising "the fee for ax^2 is barely one". of direction you may complete the sq.. f(x) = -(x^2 - 10x) to end the sq. for x^2 - 10x, i might desire to characteristic 25. using minus sign, which skill i'm particularly subtracting 25, so i might desire to characteristic 25 outdoors the parentheses. f(x) = -(x^2 - 10x + 25) + 25 = -(x - 5)^2 + 25
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Verified answer
f(x) = (3x^2 - 30x) + 82
f(x) = 3(x^2 - 10x) + 82
10 / 2 = 5
5^2 = 25
f(x) = 3(x^2 - 10x + 25) + 82 - 75
Remember that you're adding 3*25 to complete the square, so you have to subtract it as well.
f(x) = 3(x - 5)^2 + 7
So the vertex is (5,7)
Factor out the 3 first:
f(x)=3(x^2-10x+82/3)
Divide both sides by 3
f(x)/3=x^2-10x+82/3
Subtract 82/3 from both sides
f(x)/3-82/3=x^2-10x
Complete the square by taking half of 10x and squaring that :(-5)^2=25
Add 25 to both sides
f(x)/3-82/3+25=x^2-10x+25
Factor
f(x)/3-82/3+25=(x-5)^2
Multiply both sides by 3 to eliminate fractions
f(x)-82+76=3(x-5)^2
Combine like terms
f(x)-6=3(x-5)^2
Add 6 to both sides
f(x)=3(x-5)^2+6
Vertex : (5,6)
i don't understand what you advise by utilising "the fee for ax^2 is barely one". of direction you may complete the sq.. f(x) = -(x^2 - 10x) to end the sq. for x^2 - 10x, i might desire to characteristic 25. using minus sign, which skill i'm particularly subtracting 25, so i might desire to characteristic 25 outdoors the parentheses. f(x) = -(x^2 - 10x + 25) + 25 = -(x - 5)^2 + 25