GRADE 10 ACADEMIC MPM 2 D UNIT 3

QUADRATIC RELATIONS A quadratic relationship is modeled by when this relationship is graphed; the

SHAPE OF A QUADRATIC RELATION direction of opening – this parabola opens upwards. -2

SHAPE OF A QUADRATIC RELATION this parabola opens downwards 2 nd differences negative the

Example 1: Solving Quadratic Equation Solve the equation These are questions given Quadratic in

Example 2 a: Quadratic Relations (Given Factored Form) Determine the vertex, axis of symmetry,

Example 2 b: Quadratic Relations (Given Standard Form) Determine the vertex, axis of symmetry,

Example 2 c: Quadratic Relations (Given Standard Form) Determine the vertex, axis of symmetry,

HOMEWORK Work sheet: Properties of Quadratic Relations Text: P. 266 #1, 3 – 5,

END OF LESSON Properties of Quadratic Relations © 2017 E. Choi – MPM 2

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QUADRATIC RELATIONS A quadratic relationship is modeled by when this relationship is graphed; the graph of a quadratic relationship is called a parabola. Cut parallel to slant Properties of Quadratic Relations © 2017 E. Choi – MPM 2 D - All Rights Reserved

SHAPE OF A QUADRATIC RELATION direction of opening – this parabola opens upwards. -2 nd differences are positive the x-intercepts or the zeros of the relation. These values may not exist. the vertex – the point where the graph “changes direction” axis of symmetry when a parabola opens upwards, the y co-ordinate of the vertex represents the minimum value of the relation. It is the lowest point on the graph. Properties of Quadratic Relations © 2017 E. Choi – MPM 2 D - All Rights Reserved

SHAPE OF A QUADRATIC RELATION this parabola opens downwards 2 nd differences negative the y co-ordinate of this vertex would represent the maximum value of this relation. It is the highest point on this graph. Properties of Quadratic Relations © 2017 E. Choi – MPM 2 D - All Rights Reserved

Example 2 a: Quadratic Relations (Given Factored Form) Determine the vertex, axis of symmetry, the zeros (x-intercepts), and y -intercept for the following quadratic relation. Sketch the parabolas. Substitute the axis of symmetry value into given relation. Quadratic Relation to Quadratic Equation Quadratic Relation in Factored form Quadratic Relation in Standard form Properties of Quadratic Relations © 2017 E. Choi – MPM 2 D - All Rights Reserved

Example 2 b: Quadratic Relations (Given Standard Form) Determine the vertex, axis of symmetry, the zeros (x-intercepts), and y -intercept for the following quadratic relation. Sketch the parabolas. Quadratic Relation to Quadratic Equation Quadratic Relation in Standard form Quadratic Relation in Factored form Properties of Quadratic Relations © 2017 E. Choi – MPM 2 D - All Rights Reserved

Example 2 c: Quadratic Relations (Given Standard Form) Determine the vertex, axis of symmetry, the zeros (x-intercepts), and y -intercept for the following quadratic relation. Sketch the parabolas. Quadratic Relation to Quadratic Equation Quadratic Relation in Standard form Quadratic Relation in Factored form Properties of Quadratic Relations © 2017 E. Choi – MPM 2 D - All Rights Reserved