points of intersection on the x axis?

Question

determine, by considering the discriminant, the number of points of intersection with the x axis of the following parabolas

1)y=x^2-7x+3

2)y=5-7x-2x^2

3)y=3x+2x^2

Answer 1

Let m = b^2 - 4*a*c.

If m < 0 then the parabola will not intersect the x-axis.

If m = 0, then the parabola touches the x-axis at one point.

If m > 0, then the parabola intersects the x-axis at two points.