Factored form (of a quadratic)
SAT glossary · Math
Definition
The form y = a(x-r)(x-s), which displays the x-intercepts r and s as constants — in context, the times or values at which the quantity hits zero. The trap is a partial factoring such as -16(t^2-4t-5), which displays nothing: -5 is a root of the bracket, not of the function.
Factored form (of a quadratic) in plain English
The factored form of a quadratic, y=a(x-r)(x-s), is powerful because it directly displays the two x-intercepts — the values r and s where the graph crosses zero — as plain constants you can just read off. In a real-world context (like height over time), these are the exact moments the quantity hits zero. The trap to watch for is a PARTIALLY factored expression, like -16(t^2-4t-5) — this looks factored, but the piece inside the parentheses is still a polynomial, not two separate factors, so it doesn't actually display any roots yet. You'd have to factor t^2-4t-5 further into (t-5)(t+1) before the roots become visible; stopping halfway shows you nothing useful.
Also called: of a quadratic
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