SOLUTION: hi please help me to answer this general to standard form. y = 2x² - 4x + 1 Thank you

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Question 1198223: hi please help me to answer this general to standard form. y = 2x² - 4x + 1
Thank you
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!


standard form of a quadratic equation:
y+=+a%28x+-+h%29%5E2+%2B+k
you have
y+=+2x%5E2+-+4x+%2B+1.......complete square
y+=+%282x%5E2+-+4x%29+%2B+1
y+=+2%28x%5E2+-+2x%2Bb%5E2%29+-2b%5E2%2B+1........b=-2%2F2=-1
y+=+2%28x%5E2+-+2x%2B1%5E2%29+-2%2A1%5E2%2B+1
y+=+2%28x+-+1%29%5E2+-2%2B+1
y+=+2%28x+-+1%29%5E2+-1

Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Given equation: y = 2x^2-4x+1

It is of the form y = ax^2+bx+c
a = 2
b = -4
c = 1

Use the first two values to find that
h = -b/(2a)
h = -(-4)/(2*2)
h = 1
This is the x coordinate of the vertex (h,k)

Plug this into the given equation to find the y coordinate of the vertex.
y = 2x^2-4x+1
y = 2(1)^2-4(1)+1
y = -1
Therefore k = -1 is the y coordinate of the vertex (h,k)

Vertex = (h,k) = (1,-1)
This represents the lowest point on the parabola.
We know the parabola opens upward because a > 0.

Summary:
a = 2
h = 1
k = -1
Vertex form y = a(x-h)^2+k then leads to y = 2(x-1)^2-1

Graph:

I recommend using free graphing tools like Desmos and GeoGebra.
Or you can use a TI83 or TI84 calculator (or similar).