Solve simple linear-quadratic systems algebraically and graphically.
Solve a linear-quadratic system by substituting the line into a factored quadratic
Problem
Solve \(y=(x-1)(x-4)\) and \(y=0\) using the factored form. Set each factor equal to zero and include \(y=0\) when writing both intersections as ordered pairs.
Big Picture
What this problem is really about
The horizontal line supplies the shared output, and substituting it leaves the quadratic in ready-to-use factored form. We’ll apply the zero-product property to both factors, solve for every x-coordinate, then attach the line’s fixed y-coordinate and verify the resulting intersections.
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