# How do you find the vertex and intercepts for #y = 3x^2 + 12x + 5#?

##### 1 Answer

**Vertex**

The vertex is easily determined by completing the square.

In vertex form,

Therefore, the vertex is at

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**Intercepts:**

*y intercept:*

#y = 5 -> (0, 5)

*x intercept:*

Therefore, there is no x intercept.

The graphical representation of this function proves that there is no x intercept.

graph{y = 3(x + 2)^2 + 3 [-22, 21.99, -11, 11]}

We could have also found, by intuition, that there are no x intercepts: In a quadratic function

I hope you have learned a lot and that my answer was of great help.