text: what is the # of  x-intercept of the function y= -3x^2 + x - 4 ?   a quadratic function can have 0,1,or 2 x-intercepts. put a negative parabola (opens downward) over the cartesian plane and move it around. you'll see that 0 intercepts occur if the parabola is completely in the negative y part of the plane, 1 intercept occurs only in the special case where the vertex of the parabola is also a (double) root of the parabola, and two roots occur if any part of the parabola is positive. so in other words, find out where your vertex is! for parabola y(x)=ax^2+bx+c, the vertex is at the point x=-b/(2a). note that you can also complete the square to get the same information. a third route is to use the quadratic formula to see how many real roots the function has, which is how many times it touches the x-axis. use whichever method seems easiest to you at the time.