Zeros of parabola in the complex plane

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In the left Sketch you can control the shape and position of the parabola

y = a x2 + b x + c with real coefficients a, b, c
by using the Controllers below the graph. In the right hand side Sketch you see the zeros of that parabola in the complex number plane.

Parabola and the coefficient controllers Zeros in the complex plane Problems
How do the zeros change when you:

1. Change c from negative to positive, keeping a = 1 and b = 0 ?

2. Change a from positive to negative, keeping b = 0 and c = -1 ?

3. Change b from negative to positive, keeping a = 1 and c = 1 ?

4. How many real number solutions has the equation -0,53 x2 - 1,86 x - 1,37 = 0 ?
one two no real solutions

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Updated 14.3.2016