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ELEN [110]
3 years ago
5

To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you use the process of completing the square

. Let's see an example. Convert y = 2x2 - 4x + 5 into vertex form, and state the vertex.
Mathematics
1 answer:
ladessa [460]3 years ago
5 0
Since we will be completing the square we need to isolate the x

y-5 = 2x^2 -4x

now we the coefficient of the x^2 to equal 1 so we take 2 as common factor

y-5 = 2(x^2 -2x)

now we'll make it perfect square by adding 2 to both sides

y-5+2=2(x^2-2x+1)

now simplify and convert the right side to squared expression

y-3 = 2(x-1)^2

now isolate the y

y = 2(x-1)^2 +3   that's it
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\displaystyle\\&#10;1 \frac{2}{5} +\Big(-5 \frac{1}{2} \Big) = ? \\  \\ &#10;1 \frac{2}{5} = \frac{1\times 5+2}{5}=\boxed{\frac{7}{5}} \\  \\ &#10;-5 \frac{1}{2} =-5 -\frac{1}{2} = \frac{-5\times2-1}{2} =\frac{-10-1}{2}=\frac{-11}{2}= \boxed{-\frac{11}{2} }\\  \\ \texttt{OR} \\  \\ &#10;-5 \frac{1}{2} = -\Big(5 \frac{1}{2} \Big)= -\Big( \frac{5\times2+1}{2} \Big)=-\Big( \frac{11}{2} \Big)= \boxed{-\frac{11}{2} }


\displaystyle\\&#10;\Longrightarrow ~~1 \frac{2}{5} +\Big(-5 \frac{1}{2} \Big) =\frac{7}{5} -\frac{11}{2} = \frac{7\times 2}{5\times 2} -\frac{11\times 5}{2\times 5} = \\  \\ &#10;= \frac{14}{10} -\frac{55}{10} = \frac{14-55}{10} =\frac{-41}{10} = -\frac{41}{10}=-\frac{40+1}{10}=\boxed{\boxed{-4\frac{1}{10}}}



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