Creating a Parabola

Question

Using the function f(x) = 9x^2 + 12x + 4 find the vertex and the equation of axis of symmetry for the parabola.

 

(The zeros of this function are (-2,0) and (-2,0) )

 

Using the formula: x = - b/2(a)   *where b = 12 and 9 = a* how do I find the vertex and the equation of axis of symmetry?

Answer 1

You already have all of the information you need; x=-b/2a would be the x value of the vertex. So plugging in what you get for that will supply you with the y value.

 

You are correct that b=12 and a=9, so x=-12/(2*9) = -12/18 = -2/3

 

If you look at any parabola, the axis of symmetry is the vertex. So the axis of symmetry is x=-2/3

 

since f(x)=9x^2 + 12x +4,

f(-2/3)=9(-2/3)^2 +12(-2/3) +4

          =9(4/9) - 8 +4

          = 4+4-8

          =0

 

So the vertex is at (-2/3,0)