Quadratic Equations equation, roots, plots Alamgir Hossain Assistant Professor (on study leave) Department of Mathematics Jagannath University, Bangladesh December 13, 2016 Alamgir Hossain Quadratic Equations December 13, 2016 1 / 8
Outline About quadratic equation and roots 1 Roots of quadratic equation in a table 2 Plots 3 Alamgir Hossain Quadratic Equations December 13, 2016 2 / 8
About quadratic equation and roots Quadratic Equations When a � = 0, quadratic equation [1] ax 2 + bx + c = 0 has two roots and they are √ b 2 − 4 ac x = − b ± . 2 a Alamgir Hossain Quadratic Equations December 13, 2016 3 / 8
About quadratic equation and roots Type of Roots Discriminant d = b 2 − 4 ac d ≥ 0; roots are real d > 0; roots are real and distinct d = 0; roots are real and same d < 0; roots are complex Alamgir Hossain Quadratic Equations December 13, 2016 4 / 8
About quadratic equation and roots Vertex of Parabola ax 2 + bx + c y = x 2 + 2 × b 2 a x + c � � = a a � 2 − b 2 x + b � = a 4 a + c 2 a � 2 a , c − b 2 � − b Vertex of the parabola, y = f ( x ) is . 4 a Alamgir Hossain Quadratic Equations December 13, 2016 5 / 8
Roots of quadratic equation in a table Table: Type of roots d = b 2 − 4 ac comment about roots d > 0 roots are real and distinct d = 0 roots are real and same d < 0 roots are complex Alamgir Hossain Quadratic Equations December 13, 2016 6 / 8
Plots Plots of quadratic equations Figure: LaTex: Quadratic Functions Alamgir Hossain Quadratic Equations December 13, 2016 7 / 8
Plots Reference Howard Anton, Irl Bivens, and Stephen Davis. Calculus , volume 2. Wiley Hoboken, 2002. Alamgir Hossain Quadratic Equations December 13, 2016 8 / 8
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