Answer:
For the equation of any graph. The graph intercepts the y-axis, when x is zero, so in the equation, substitute x=0, and solve for y. To find the x-intercept, this is when y is zero, so substitute y=0, and solve for x.
For a parabola, if the highest power of y is the 1st power (no exponent) and the highest power of x is 2, then the parabola opens up or down. The parabola will have 1 y-intercept (usually it is the constant value), and depending on where it is (if it is at the origin, it is also an x-intercept, and the other x-intercept has the same distance as y-intercept has from the axis of symmetry i.e y = a2x + bx), either have 2 x-intercepts, or no interceptions with the x-axis (i.e. y = x2 + c, c ≥ 0 or y = -x2 + c, c ≤ 0).
If the highest power of y is 2, and highest power of x is 1, then it opens left or right, and it may have none or 2 y-intercepts, and will have 1 x-intercept.
So when you're solving for the one that's a quadratic, if you come up with imaginary or complex roots, that means there is no intercept.