what happens if you go from y= x^2 + 1 to y= -x^2 + 1, what happens to the parabola?

Let me just add to what reinout said....if we took the second derivative of the first function, we get "2," which indicates that the curve is concave upward, and the second derivative of the second function = -2, which indicates the curve is concave downward.

And as Melody indicated, both parabolas share the same vertex - (0,1).

You can remember this by heart but you can also derive this.

if $$y = x^2 + 1$$ then $$\frac{dy}{dx} = 2x$$ which shows $$\frac{dy}{dx} \geq 0$$ if $$x \geq 0$$ and $$\frac{dy}{dx} \leq 0$$ if $$x \leq 0$$

Hence the curve first goes down and then up which makes it a cup form.

Similarly

if $$y = -x^2 + 1$$ then $$\frac{dy}{dx} = -2x$$ which shows $$\frac{dy}{dx} \leq 0$$ if $$x \geq 0$$ and $$\frac{dy}{dx} \geq 0$$ if $$x \leq 0$$

Hence the curve first goes up and then down which makes it a cap form.

Reinout 

Reinout is right ofcourse - but my goodness, what a lot of explaination!  

It's simple. 

The parabola just gets flipped upside down!