Grade 10 Academic (MPM2D) Unit 4: Quadratic Relations Discriminants of Quadratics Mr. Choi © 2017 E. Choi – MPM2D - All Rights Reserved.

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Grade 10 Academic (MPM2D) Unit 4: Quadratic Relations Discriminants of Quadratics Mr. Choi © 2017 E. Choi – MPM2D - All Rights Reserved

Summary: Quadratic Formulas Vertex Form: Axis of Symmetry: x-intercepts: y-intercept: Standard Form: Vertex: Axis of Symmetry: x-intercepts: y-intercept: Discriminants of Quadratics © 2017 E. Choi – MPM2D - All Rights Reserved

Quadratic formula is used to find the roots of the quadratic relation Recall: Quadratic formula is used to find the roots of the quadratic relation To find the roots: let and , then Note that in the quadratic formula, the value of determines the number and type of roots a quadratic equation has. This expression is called the discriminant. 2 real roots 1 real root no real roots When using the quadratic formula, If then the quadratic equation has 2 real roots. If then the quadratic equation has 2 equal real roots (1 real root). If then the quadratic equation has No real roots. Discriminants of Quadratics © 2017 E. Choi – MPM2D - All Rights Reserved

Example 1: Discriminants Determine how many roots each equation has Discriminants of Quadratics © 2017 E. Choi – MPM2D - All Rights Reserved

Example 1: Discriminants Determine how many roots each equation has Different thinking!! (7, -12) Different thinking 2!! Vertex: (7, -12) Vertex form: Since the vertex is (7, -12) and the parabola is opens up, therefore there are two zeros. The equation has two roots. Discriminants of Quadratics © 2017 E. Choi – MPM2D - All Rights Reserved

Example 2: Discriminant For , determine how many x-intercepts each relation has. Determine the key features (intercepts, axis of symmetry, vertex) of the parabola. Sketch the parabola. Method 1: Method 2: 2 equal real roots Or 1 real root at x = 2. x- intercepts: y - intercept: Axis of symmetry: Vertex: Discriminants of Quadratics © 2017 E. Choi – MPM2D - All Rights Reserved

Homework Work sheet: Discriminants of Quadratics: Functions and Relations Text: P. 403 #5 Check the website for updates Discriminants of Quadratics © 2017 E. Choi – MPM2D - All Rights Reserved

End of lesson Discriminants of Quadratics © 2017 E. Choi – MPM2D - All Rights Reserved