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Firdavs [7]
3 years ago
8

PLLLLLSSSS Heeeellppp ill mark brainliest I promisseeeeeeee plsssss

Mathematics
1 answer:
WARRIOR [948]3 years ago
5 0

Answer:

2\,(x-1)^2=4

which is the first option in the list of possible answers.

Step-by-step explanation:

Recall that the minimum of a parabola generated by a quadratic expression is at the vertex of the parabola, and the formula for the vertex of a quadratic of the general form:

y=ax^2+bx+c

is at   x_{vertex}=\frac{-b}{2\,a}

For our case, where a=2\,\,, b=-4\,\,,\,\,and \,\,c=-2  we have:

x_{vertex}=\frac{-b}{2\,a}\\x_{vertex}=\frac{4}{2\,*\,2}\\x_{vertex}=1

And when x = 1, the value of "y" is:

y(x)=2x^2-4x-2\\y(1)=2(1)^2-4(1)-2\\y(1)=2-6\\y(1)=-4\\y_{vertex}=-4

Recall now that we can write the quadratic in what is called: "vertex form" using the coordinates (x_{vertex},y_{vertex)of the vertex as follows:

y-y_{vertex}=a\,(x-x_{vertex})^2

Then, for our case:

y-(-4)=2\,(x-1)^2\\y=2\,(x-1)^2-4

Then, for the quadratic equal to zero as requested in the problem, we have:

y=2\,(x-1)^2-4=0\\2\,(x-1)^2-4=0\\2\,(x-1)^2=4

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