Quadratic Equation Solution Example

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2014-09-13 01:39

In collections UCSS Secondary Math II Unit 3B Lesson 2

This example demonstrates solving the quadratic equation [math]5x^2 + 2x + 1 = 0[/math]. It involves core math concepts like quadratic equation solving, discriminant, and complex roots. GeoGebra commands and objects used include GCD, Product, TableText, and elements like an3, an1, an2, comFact, c, b, a, step, explain3b, DirectionsSlider, disc, f, discSqrFree, discSqrTerm, imPt, rePt, Directions3, Directions0, Directions1, Results3, Directions2, Directions4, Work3. Suitable for high school mathematics teaching, illustrating the method and geometric meaning of quadratic equation solutions.

GeoGebra Commands & Parameters

GCD({an3^(2), ((2 * an1) * an3), an1^(2) + an2^(2)}) → comFact
Product(Zip[Element[f, 1]^(Mod[Element[f, 2], 2]), f, Factors[(-disc)]]) → discSqrFree
TableText({{"x=\frac{-b\pm\sqrt{(b)^2-4(a)( c )}}{2(a)}", "\text{Quadratic formula}"}, {"x=\frac{-" + b + "\pm\sqrt{(" + b + ")^2-4(" + a + ")(" + c + ")}}{2(" + a + ")}", "\text{Substitute into the quadratic formula.}"}, {"x=\frac{-" + b + "\pm\sqrt{" + (b^(2)) + "-" + (((4 * a) * c)) + "}}{" + ((2 * a)) + "}", "\text{Simplify.}"}, {"x=\frac{-" + b + "\pm\sqrt{" + disc + "}}{" + ((2 * a)) + "}", "\text{Simplify under the radical.}"}, {"x=\frac{-" + b + "\pm" + discSqrTerm + " i}{" + ((2 * a)) + "}", "\text{Simplify }\sqrt{" + disc + "}\text{.}"}, {"x=" + rePt + "\pm " + imPt + "i", "\text{Divide the fractions}."}}) → Work3

AI Drawing Prompt Reference

Draw the graph of the quadratic equation 5x^2 + 2x + 1 = 0 and show the discriminant and complex roots. First, plot the graph of the quadratic equation, then mark the discriminant disc, calculate and display the solutions of the quadratic equation, including real and imaginary parts. Finally, explain the geometric meaning of the solutions in text.

The prompt above was compiled from the original drawing commands and is for reference only.