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"y = 2x2 - 12x + 6" is a quadratic equation which describes a parabola whose vertex occurs at the point (3, -12) and which has a range of -12 → ∞. It intercepts the x-axis at the points (3 - √6, 0) and (3 + √6, 0).
y=4x-12-3 is the equation of a straight line. It does not have a vertex. Did you mean y=x squared - 12x - 3 ?
y2-12=5x is an equation. When graphed, it is a parabola.
The x-intercept of an equation is any location where on the equation where x=0. In the case of a parabolic function, the easiest way to obtain the x intercept is to change the equation into binomial form (x+a)(x-b) form. Then by setting each of those binomials equal to zero, you can determine the x-intercepts.
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