How can you tell from a quadratic function if on a graph it would open upwards or downwards?

Question

y=-3x² + 4x  Or y+2=x²

Answer 1

y=x² opens upwards. 

 

Deciding whether another quadratic equation's graph will also open upwards or downwards is a question of transformation. When the equation is in standard form, y=ax²+bx+c, then the graph will open upwards if and only if "a" is positive.

Answer 2

You would take the 2nd derivative of the function. So for y=-3x^2 +4x, the 1st derivative would be -6x, and the 2nd derivative would be -6. 

 

Now once you have the 2nd derivative, you see if it is positive or negative. If it is positive, then it opens upward. If it is negative, then it opens downward.

 

Hope that helps!