Respuesta :
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.
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,
[tex]y = 2x^2 -4x + 12[/tex]
Column Two states that,
The x-coordinate of the vertex of the equation,
[tex]y = 4x^2 + 8x + 3[/tex]
Coordinate vertex
Coordinate vertex is the point at which the parabola crosses its axis of symmetry.
For the standard quadratic equation of parabola,
[tex]ax^2+bx+c[/tex]
The x coordinate of the vertex for the above equation is,
[tex]\dfrac{-b}{2a} [/tex]
Let the first equation;
[tex]y = 2x^2 -4x + 12\\ [/tex]
Compare this equation with standard equation we get,
[tex]\dfrac{-b}{2a} =\dfrac{-(-4)}{2\times2}\\ \dfrac{-b}{2a}=1[/tex]
Thus the value of the column 1 is 1.
The second equation,
[tex]y = 4x^2 + 8x + 3 [/tex]
Compare this equation with standard equation we get,
[tex]\dfrac{-b}{2a} =\dfrac{-8}{4\times2}\\ \dfrac{-b}{2a}=-1[/tex]
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
