Question

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 The x-coordinate of the vertex of the equation
y=2x² – 4x + 12
y = 4x² + 8x +3
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.

1. quangkhai
The equation shows that value found in column #1 is less than the value found in column #2.

How to illustrate the information?

y = 2x² – 4x + 12
= -2(2x² + 2x) + 12
= -2(x² + 2x + 1) + 12
= -2(x + 1)² + 14
y = x² – 4x + 3
= (x² – 4x) + 4
= (x² – 4x + 4) + 3 – 4.
= (x – 2)² – 1
The vertex is (-1, 14) and (2, -1) for 1 and 2 respectively.
Therefore, the equation shows that value found in column #1 is less than the value found in column #2.