Create your own unique quadratic equation in the form y = ax^2 + bx + c. Use complete sentences and show all work to determine the following:

Does the graph open up or down? How do you know?
Explain whether the graph has a maximum or minimum point.
Find the vertex and x-intercepts of the graph.

Question

Create your own unique quadratic equation in the form y = ax^2 + bx + c. Use complete sentences and show all work to determine the following:

Does the graph open up or down? How do you know? 
Explain whether the graph has a maximum or minimum point. 
Find the vertex and x-intercepts of the graph.

anonymous · Answer

Form: $y=ax^2+bx+c$. For $a>0$, this opens up, since a positive coefficient in front of the leading term means the limits go to $+\infty$.

Imagine a parabola in your head. If the graph opens up, the maximum is undefined at $\infty$, while the minimum is a specific point, right?

The last part should be relatively straightforward. For ease, I suggest you pick $(x+1)^2$. And laugh as you skip most of the work.