Hey,
      I was wondering if somebody could help me with this. I want the mouse location to be the vertex of my parabola and one of the x intercepts to be in the bottom left hand corner of the screen.

THX,
     The Lonckinator

it is possible... try this code

//only executes the animation once so not really animation
// create variable by by using float and then name and thin under use the name with what it should =
float targetx;
float targety;

void setup() {
  size (400, 400);
  smooth();
frameRate(30);
targetx = random(200, 375);
 targety = random(200, 375);
}

//
void draw(){

{  background (0);
stroke(0);

 fill(255, 0, 0);
 ellipse(targetx, targety, 50, 50);

fill(255);
ellipse(targetx , targety, 35, 35);

fill(255, 0, 0);
ellipse(targetx, targety, 20, 20);

fill(255);
ellipse(targetx , targety, 5, 5);

float x = 0; //our first point will be at x=0
float y = height;


beginShape();
while(y <= height) {
 float a = (height - mouseY) / (mouseX * mouseX + 0.01);
 y = a * (x - mouseX) * (x - mouseX) + mouseY;
 vertex(x, y);
 x += 0.1;
}
endShape();
}
 }
void mousePressed(){

 targetx = random(200, 375);
 targety = random(200, 375);
 
}