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) (Show Source): You can put this solution on YOUR website!
standard form of a quadratic equation:
you have
.......complete square
........
Answer by math_tutor2020(3816) (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).
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