We can see from the graph that the parabola intersects the x-axis (the line y = 0) at x = 2 and x= 6. We can sometimes find the solutions of a quadratic equation by graphing and finding the x-intercepts (zeros). Example: Solving A Quadratic Equation By GraphingĬonsider the following parabola (the graph of a quadratic): To solve a quadratic equation by graphing, all we really need to do is find out where the zeros are (the points where the graph intersects the x-axis). How To Solve Quadratic Equations By Graphing Let’s take a look at some examples of each method, starting with graphing. If r and s are real, we also have x-intercepts for the parabola, which makes it easier to graph. If we take the average of the two solutions r and s, we can find the x-coordinate of the parabola’s vertex (that is, the axis of symmetry).If we use the coefficient ‘a’ together with the solutions r and s, we can write the factored form of the quadratic equation as a(x – r)(x – s) = 0.These solutions may be distinct and real (positive discriminant), double real (zero discriminant), or complex conjugates (negative discriminant). When we use the quadratic formula on a quadratic equation, we get two solutions to the equation: r and s.
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