# How do you find the vertex and the intercepts for #f(x)=3x^2-12x+15#?

##### 1 Answer

Vertex:

#### Explanation:

To find the vertex convert the given equation into vertex form.

which is the vertex form for a parabola with vertex at

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

The

Using the original form of the equation we can see that

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

The

Using the vertex form we derived

Since the square of any Real number is greater than or equal to zero

we can see that this equation has no Real solutions.

However if Complex solutions are permitted

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

For verification purposes, here is a graph of the original equation:

graph{3x^2-12x+15 [-21.36, 19.18, -0.08, 20.21]}