Determine the vertex and the direction of opening for each quadratic function. Then state the number ...

Hi there, this is an incomplete quadratic, meaning that it doesn't have a constant at the end of it. To find the zeros, you could use the quadratic formula, but it's not required for incomplete quadratics. Just set f(x) = 0, like this:

\(f(x)=3(x+2)^2\)

\(0=3(x+2)^2\)

Divide both sides by 3:

\(\frac{0}{3}=\frac{3(x+2)^2}{3}\)

Simplifies to:

\(0=(x+2)^2\)

Now we square root both sides:

\(\sqrt{0}=\sqrt{(x+2)^2}\)

\(0=x+2\)

Solve for x:

\(x=-2\)

There is only one root.

If you'd like me to show you using the quadratic formula, let me know, reply back

Thank you so much, but the thing that I don't get is how -2 is 1 root, shouldn't it be no roots because it is a negative?

When you find -2 as a root, it means that you'll have a point along the x-axis that has the coordinates (-2, 0).

Here's what I mean looking at it graphically [see attachment]

I've also attached a video of how it's done for another example...

Thank you so much, I really appreciate it!

Happy to help