How do you solve this Algebra 2 problem?

Question

In order to transform the vertex of y=x^2+4x+4 to the orgin, every point must be translated: a) 2 units left, b) 2 units right, c) 4 units left, d) 4 units right

Answer 1

 Basic equation was

 

Y = X^2:              Y =   X ^2 + 4 X + 4 = ( X +2 ) ^2

 

 Y   = ( X + 2 ) ^2  

 

   X shifts 2 units to the left .

Answer 2

In order to transform the vertex of y=x^2+4x+4 to the origin, every point must be translated: a) 2 units left, b) 2 units right, c) 4 units left, d) 4 units right

 

First, you need to find out where the vertex is.  The x-coordinate of the vertex lies at x = -b/2a, where b is the coefficient of the x term and a is the coefficient of the x² term

 

x = -b/2a = (-4)/2(1) = -2

 

Plug in x = -2 to find the y-coordinate of the vertex

 

y = (-2)² + 4(-2) + 4 = -4 + 8 -4 = 0

 

Hence the vertex lies at (-2,0)

 

              Vertex

              (-2,0)

--|----|----*----|----|----|--

 -4    -3    -2    -1      0     1

                 |_________↑

 

To move the vertex to (0,0), you have t move it 2 units to the right. = b)