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 graph of y = −2x2 − 4x + 12 The x-coordinate of the vertex of the graph of y = x2 − 4x + 3

Answer 1

Answer with explanation:

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

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

So, Coordinate of vertex can be obtained by

→ x+1=0

x= -1

and, $\frac{-y}{2}+7=0\\\\ y=14$

is equal to , (-1,14).

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

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

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

So, Coordinate of vertex can be obtained by

→ x-2=0

x= 2

and, →y+1=0

y= -1

is equal to , (2,-1).

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

Answer 2

Hi,


1)
 $y=-2x^2-4x+12=-2(x^2+2x+1)+2+12=-2(x+1)^2+14\\\\ Vertex=(-1,14) \ x-coordinate=-1$


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