Question

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

Column #1
The x-coordinate of the vertex of the graph of y = −2x2 − 4x + 12

Column #2
The x-coordinate of the vertex of the graph of y = x2 − 4x + 3

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

Answer 1

The following statements are true concerning the values described in columns #1 and column #2. B. The value found in column #1 is less than the value found in column #2.

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree

The equation of curve 1, which is in the shape of a parabola is, when represented in general form

$y = -2x^2 - 4x + 12\\\\y = -2(x^2 - 2x + 6)\\\\\dfrac{y}{-2} = (x^2 - 2x + 6)\\\\\dfrac{y}{-2} +7=(x+1)^2$

So,

x+1=0

x= -1

and,

y = 14

Therefore, the Coordinate of a vertex is (-1,14).

The x-coordinate of the vertex of the function $y = -2x^2 - 4x + 12$ is equal to -1.

The equation of curve 2 , which is in the shape of a parabola is , when represented in general form

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

So,

x-2=0

x= 2

and, y+1=0

y= -1

Therefore, the Coordinate of a vertex is (2,-1).

The x-coordinate of the vertex of the function $y = x^2 - 4x + 3$ is equal to 2.

The following statements are true concerning the values described in columns #1 and column #2. B. The value found in column #1 is less than the value found in column #2.

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