In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

Question

y= 9x²+ 12x+ 4

 

How do i solve this problem step by step?

Answer 1

1. Factor to find the x-intercepts.

 

9x² + 12x + 4

(3x + 2)(3x + 2)

 

3x + 2 = 0

3x = -2

x = -2/3

 

2. Find the axis of symmetry (x = -b/2a).

 

x = -b/2a

x = -12/18

x = -2/3

 

3. Use the equation for the axis of symmetry as the x-component of your vertex.  Plug this value in to the initial equation to find the y-component of the vertex.  Because there is only one x-intercept, you know this must be the vertex, so (-2/3,0) is the vertex.