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Determine which of the following statements is true concerning the values described in column #1 and column #2.





Column #1


Column #2



The x-coordinate of the vertex of the equation

y = 2x2 − 4x + 12 The x-coordinate of the vertex of the equation

y = 4x2 + 8x + 3

Verified Answer :

MissPhiladelphia

Below are the choices:

The value found in column #1 is greater than the value found in column #2. 
The value found in column #1 is less than the value found in column #2. 
The value found in column #1 is equivalent to the value found in column #2. 
The relationship between column #1 and column #2 cannot be determined by the information given. 

 y = -2x^2 - 4x + 12 = -2(x^2 + 2x) + 12 = -2(x^2 + 2x + 1) + 12 + 2 = -2(x + 1)^2 + 14 

y = x^2 - 4x + 3 = (x^2 - 4x) + 3 = (x^2 - 4x + 4) + 3 - 4 = (x - 2)^2 - 1 

The vertex is (-1, 14) in the first; (2, -1) in the second. 

column 1 value is less than column 2 value. 

Coordinate of vertex is the point at which the parabola crosses its axis of symmetry. The value of the column 2 is less than the value of the column 1.

Given information-

Column one states that,

The x-coordinate of the vertex of the equation is,

\(y = 2x^2 -4x + 12\)

Column Two states that,

The x-coordinate of the vertex of the equation,

\(y = 4x^2 + 8x + 3\)

Coordinate vertex

Coordinate vertex is the point at which the parabola crosses its axis of symmetry.

For the standard quadratic equation of parabola,

\(ax^2+bx+c\)

The x coordinate of the vertex for the above equation is,

\(\dfrac{-b}{2a}\)

Let the first equation;

\(y = 2x^2 -4x + 12\\\)

Compare this equation with standard equation we get,

\(\dfrac{-b}{2a} =\dfrac{-(-4)}{2\times2}\\ \dfrac{-b}{2a}=1\)

Thus the value of the column 1 is 1.

The second equation,

\(y = 4x^2 + 8x + 3\)

Compare this equation with standard equation we get,

\(\dfrac{-b}{2a} =\dfrac{-8}{4\times2}\\ \dfrac{-b}{2a}=-1\)

The value of the column 2 is -1

Hence the value of the column 2 is less than the value of the column 1.

Learn more about the coordinate of vertex here;

https://brainly.com/question/20324620

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