Question

Determine the equation of the parabola that cuts x axis in points A(-7,0) and B(1/2,0)?

Answer 1

That's a quadratic with zeros `-7` and `1/2;` there are many, but only one monic:

`y = (x - -7)(x - 1/2) = x^2 + 13/2 x - 7/2`

The minimal polynomial has integer coefficients with no common factors:

`y = 2 x^2 + 13 x - 7`

Explanation:

graph{0=( 2 x^2 + 13 x - 7-y)(x^2+13/2 x -7/2 - y) [-42.93, 37.07, -30, 10]}