Please help with Alg. 1 Question?

Create your own unique quadratic equation in the form y = ax2 + bx + c. Use complete sentences and show all work to determine the following:

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

Question

Please help with Alg. 1 Question? 

Create your own unique quadratic equation in the form y = ax2 + bx + c. Use complete sentences and show all work to determine the following:

1- Does the graph open up or down? How do you know? 
2- Explain whether the graph has a maximum or minimum point
3- Find the vertex and x-intercepts of the graph

anonymous · Answer

Which part do you need help with?

anonymous · Answer

@nbouscal  Creating my own unique quadratic equation in the form y = ax2 + bx + c

anonymous · Answer

Okay, just pick numbers for a, b, and c. Whole numbers would be easiest, but they can be positive or negative, whatever you would like.

anonymous · Answer

y = 4x2 + 2x + 8 
Okay then what do I have to do? Graph it and answer the questions?

anonymous · Answer

@nbouscal

anonymous · Answer

Sure, graphing is one approach to it, that would work.

anonymous · Answer

You can also use algebraic manipulation to answer the questions. For example, if a is positive then the graph opens upward, if it's negative then the graph opens downward.

anonymous · Answer

When I try graphing it online, it says the equation is an error @nbouscal

anonymous · Answer

You probably want it to say 4x^2, not 4x2

anonymous · Answer

I tried that but it still didn't work.. @nbouscal

anonymous · Answer

Okay. I don't know what graphing utility you're using. You can graph it by hand.

anonymous · Answer

Okay nvm, I got it. But how do I know wether the graph has a max or a min? @nbouscal

anonymous · Answer

The graph is facing up btw

anonymous · Answer

Max or min is just what it sounds like, does the graph have a maximum point or a minimum point. A peak or a valley

anonymous · Answer

So would it be a min because its facing up? @nbouscal

anonymous · Answer

Yep

anonymous · Answer

Okay! last question sorrrry lol 

How would i find the vertex and x-intercepts of the graph? 
@nbouscal

anonymous · Answer

Vertex is the minimum point. x-intercepts are the points where the graph intercepts the x axis. It's a bit tricky because your graph is completely above the x axis, so it doesn't have any x-intercepts. It does still have a vertex, though.

anonymous · Answer

Okay I got it all, thank you for your help! @nbouscal