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Making the Connection Between Graphing and Solving

We've learned two really important things in recent chapters:

 

1How to solve a quadratic = 0 :

ax^2 + bx + c = 0

2How to graph a quadratic:

y = ax^2 + bx + c

Now, let's make the connection between the two!  I'll explain it with an example:

Let's graph this guy:

y = 3x^2 - 1

y = 3x^2 - 1 ... right side up, 3 times as tall, shifted down 1

graph of y = 3x^2 - 1

But, there's one other really important thing we need to know:

Where does this guy cross the x-axis?

From our graph, it LOOKS like it might be around x = - .6 and x = .6 ...  How can we be sure?