2. Solving Quadratic Equations by Graphing
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To solve the quadratic equation ax^2+bx+c= 0, we can consider the associated quadratic function f(x)=ax^2+bx+c. Notice that the x-values for which f(x)=0 satisfy the original equation. f(x)=0 ⇔ ax^2+bx+c= 0 Since all the points on the graph are of the form (x,f(x)), the solutions to the original equation are the x-values of the points (x,0). These are the x-intercepts of the associated function.
We can summarize these ideas as shown below.
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We can solve a quadratic equation ax^2+bx+c=0 using the graph of its associated function f(x) = ax^2+bx+c and by identifying the x-intercepts of the graph. These are also the solutions to the quadratic equation. |