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9.1 Exploring Quadratic Graphs

9.1 Exploring Quadratic Graphs. Objective: SWBAT graph quadratic functions and find roots or x -intercepts. Mini Quiz 22. 2. Overview. Quadratic functions y = ax 2 + bx + c (no b for today) Identifying maximum and minimum Comparing widths of parabolas Graphing the parabola

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9.1 Exploring Quadratic Graphs

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  1. 9.1 Exploring Quadratic Graphs Objective: SWBAT graph quadratic functions and find roots or x-intercepts.

  2. Mini Quiz 22 2.

  3. Overview Quadratic functions y = ax2 + bx + c (no b for today) • Identifying maximum and minimum • Comparing widths of parabolas • Graphing the parabola • Finding the vertex

  4. Quadratic Function Standard Form: Parabola: U-shaped graph for quadratic function What is a, b, and c for the following quadratic functions? 1. y = 2x2 + 3x – 4 2. y = x2 – x + 9 3. y = -x2 – 7 Leading Coefficient Vertex- highest or lowest point on the parabola

  5. Parabola – Quadratic Functions Important “Points” x-intercepts, roots, zeros Does the graph have a maximum or a minimum? vertex (on the axis of symmetry x = #)

  6. Vertex, Axis of Symmetry, andMax or Min 1. Vertex (0, 0); x = 0; Min 2. Vertex (-2, 4); x = -2; Max 3. Vertex (4, 3); x = 4; Max 4. Vertex (1, -2); x= 1; Min Identify the vertex and axis of symmetry. Tell whether it is a minimum or maximum.

  7. Who’s the widest of them all? Widest: The “smaller” the “a” is, the wider the graph

  8. Graphing the Parabola Steps: 1. Make a T-chart 2. Find the vertex: (axis of symmetry) 3. Graph 2 points to each side of the vertex 4. Draw the parabola 5. Write the x-intercepts x = -2, x = 0 Graph: y = x2 + 2x 1 3 0 0 -1 -1 -2 0 -3 3

  9. Graph and Write the x-intercepts x = 0 x = 0 x = No Solution x = -2 x = 2

  10. Wrap Up Quadratic functions y = ax2 + bx + c (no b for today) • Identifying maximum and minimum • Comparing widths of parabolas • Graphing the parabola • Find vertex: • Pick 2 points on each side of the vertex • Graph the parabola HW: P. 429 #1-29 EOO DLUQ: What is the formula for the axis of symmetry and the vertex for the x-coordinate?

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