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Quadratic Functions and Equations

Chapter 9 . Quadratic Functions and Equations. Pg. 546 – 552 Obj : Learn how to graph quadratic functions. Content Standards: F.IF.7.a, A.CED.2, F.IF.4, F.IF.5, and F.BF.3. 9.1 Quadratic Graphs and Their Properties. Quadratic Function – a function that has a degree of two

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Quadratic Functions and Equations

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  1. Chapter 9 Quadratic Functions and Equations

  2. Pg. 546 – 552 Obj: Learn how to graph quadratic functions. Content Standards: F.IF.7.a, A.CED.2, F.IF.4, F.IF.5, and F.BF.3 9.1 Quadratic Graphs and Their Properties

  3. Quadratic Function – a function that has a degree of two Standard form of a Quadratic Function – Quadratic Parent Function – the simplest quadratic function 9.1 Quadratic Graphs and Their Properties

  4. Parabola – the graph of a quadratic function that is a U shaped curve Axis of symmetry – the line that divides the parabola into two matching halves – x=-b/2a Vertex – the highest or lowest point of a parabola Minimum – the lowest point – occurs if a>0 Maximum – the highest point – occurs if a<0 9.1 Quadratic Graphs and Their Properties

  5. Graphing a Quadratic Function • Find the axis of symmetry – x=-b/2a • Substitute the value of x into the original function and solve for y – this is the vertex • Choose two x-values on one side of the axis of symmetry and substitute those values into the original function. Solve for y. • The previous step results in two points. Graph these points and the corresponding points on the other side of the axis of symmetry. • Draw a parabola containing all of the points. 9.1 Quadratic Graphs and Their Properties

  6. Pg. 553 – 558 Obj: Learn how to graph quadratic functions. Content Standards: F.IF.7.a, A.CED.2, F.IF.4, F.IF.8.a, F.IF.9, F.BF.3 9.2 quadratic Functions

  7. Pg. 561 – 566 Obj: Learn how to solve quadratic equations by graphing and using square roots. Content Standards: A.REI.4.b, N.Q.2, A.APR.3, A.CED.1, and A.CED.4 9.3 Solving Quadratic Equations

  8. Roots of the Equation or Zeros of the Function – the x-intercepts of the graph 9.3 Solving Quadratic Equations

  9. Pg. 568 – 572 Obj: Learn how to solve quadratic equations by factoring. Content Standards: A.REI.4.b, A.SSE.3.a, A.CED.1, and F.IF.8.a 9.4 Factoring to Solve Quadratic Equations

  10. Zero Product Property – If ab = 0, then a=0 or b=0 9.4 Factoring to Solve Quadratic Equations

  11. Pg. 576 – 581 Obj: Learn how to solve quadratic equations by completing the square. Content Standards: A.REI.4.a, N.Q.3, A.SSE.1.a, A.SSE.1.b, A.SSE.3.b, A.CED.1, A.REI.1, A.REI.4.b, and F.IF.8.a 9.5 Completing the Square

  12. Pg. 582-588 Obj: Learn how to solve quadratic equations using the quadratic formula and find the number of solutions of a quadratic equation. Content Standards: A.REI.4.a, N.Q.3, A.CED.1, and A.REI.4.b 9.6 The Quadratic Formula and the Discriminant

  13. Quadratic Formula 9.6 The Quadratic Formula and the Discriminant

  14. Discriminant • Positive = two real solutions • Zero = one real solution • Negative = no real solutions 9.6 The Quadratic Formula and the Discriminant

  15. Pg. 589 – 594 Obj: Learn how to choose a linear, quadratic, or exponential model for data. Content Standards: F.LE.1.a, F.IF.4, F.LE.2, F.LE.3, and S.ID.6.a 9.7 Linear, Quadratic, and Exponential Models

  16. Pg. 597 – 601 Obj: Learn how to solve systems of linear and quadratic equations. Content Standards: A.REI.7, A.CED.3, and A.REI.11 9.8 System of Linear and Quadratic Equations

  17. 3 Methods • Graphing • Elimination • Substitution 9.8 System of Linear and Quadratic Equations

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