Solve simple linear-quadratic systems algebraically and graphically.
Interpret line-parabola intersections in context
Problem
For \(x^{2}-5x+6=0\), identify \(a\), \(b\), and \(c\) with signs, calculate \(D=b^{2}-4ac\), and use its sign to determine the number and type of real intersections.
Big Picture
What this problem is really about
The discriminant lets us classify the intersections without solving for their exact coordinates. We’ll read the signed coefficients carefully, evaluate b squared minus four a c, and translate its sign into the number and type of real x-values—and therefore graph intersections.
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