Use the vertex form of parabola equation to find out the vertices needed and then compare the x coordinate.
The correct option is: Option B: The value found in column 1 is less than value found in column 2
What is vertex form of parabola?
A quadratic equation of the form [tex]y = a(x-h)^2 + k[/tex] is called vertex form of quadratic equation. It represents a parabola with vertex at coordinate (h,k).
Finding the vertices of given parabolas
For column 1: [tex]y = -2x^2 - 4x + 12[/tex]
Converting to vertex form:
[tex]y = -2x^2 - 4x + 12\\
y = -2(x^2 +2x) + 12\\
y = -2(x^2 + 2x + 1 - 1) + 12\\
y = -2(x^2 + 2x + 1) + 2 + 12\\
y = -2(x+1)^2 + 14[/tex]
Thus, first column's parabola has vertex at h = -1, k = 14 or at (-1,14)
For column 2: [tex]y = x^2 - 4x + 3[/tex]
Converting to vertex form:
[tex]y = x^2 - 4x + 3\\
y = x^2 - 4x + 4 - 4 + 3\\
y = (x^2 -4x + 4) - 1\\
y = (x-2)^2 - 1\\
[/tex]
Thus, second column's parabola has vertex at h = 2, k = -1 or at (2,-1)
The x coordinate of vertex of parabola of first column is -1
The x coordinate of vertex of parabola of second column is 2
Thus, Option B: The value found in column 1 is less than value found in column 2 is correct.
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