1.11 Solving Equations and Inequalities Graphically
Ideas in this lesson
Solve equations by intersections
Solve zero-form equations using x-intercepts
Interpret graphical solutions in context
Solve inequalities from graphs
Approximate roots and assess viewing windows
Solve varied nonlinear graph families and respect their domains
Solve equations by intersections · Worked example
A student reads the intersection points \((0,2)\) and \((4,6)\) of the graphs below and answers “\(2\) and \(6\).” Correct the answer to \(x^{2}-3x+2=x+2\).pc1_11-G1-P1: y = x² − 3x + 2, y = x + 2
Answer: \(x=0,4\).
The equation asks for input values, which are the horizontal coordinates. The plotted intersections have x-coordinates \(0\) and \(4\). Subtracting the right side gives \(x^{2}-4x=x(x-4)=0\), independently verifying both.