Frequently Asked Questions
What is completing the square?
Rewriting ax^2 + bx + c as a(x + b/2a)^2 + (c - b^2/4a). The first piece is a perfect square trinomial scaled by a; the second piece is a constant remainder.
Are all squares of binomials perfect square trinomials?
Yes. Conversely, every perfect square trinomial is the square of some binomial. The names are used interchangeably.
What is the discriminant role?
If b^2 - 4ac = 0, the quadratic has a double root, the parabola touches the x-axis at exactly one point, and the trinomial factors as a perfect square.
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