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4.1 Notes – Graph Quadratic Functions in Standard Form

4.1 Notes – Graph Quadratic Functions in Standard Form. Parabola that is a function in the shape of a U. y = ax 2 + bx + c. Max or Min of a parabola. Line that splits the graph vertically. Transformations of a, b, and c. Opens up. Opens down. Has minimum. Has maximum.

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4.1 Notes – Graph Quadratic Functions in Standard Form

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  1. 4.1 Notes – Graph Quadratic Functions in Standard Form

  2. Parabola that is a function in the shape of a U y = ax2 + bx + c Max or Min of a parabola Line that splits the graph vertically

  3. Transformations of a, b, and c. Opens up Opens down Has minimum Has maximum a = 1, normal a = –1, normal Fraction, wide Fraction, wide a > 1, skinny a < –1, skinny

  4. Set y = 0, factor the equation and solve for x Two answers One answer No Real answers

  5. y = ax2 + bx + c Shift vertex left or right y – intercept

  6. 3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. This is the parent function.

  7. 3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. (2, 4) 2 (1,1) 1 (0,0) 0 –1 (–1,1) –2 (–2, 4)

  8. (0,0) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = 0 y = 0 0 0

  9. (0,0) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = 0 y = 0 0 0 (2, 4) (1,1) (0,0) (–1,1) (–2, 4)

  10. 1. Put the equation in standard from. Determine if the graph opens up or down and if it is normal, skinny, or wide. Standard Form: Opens up wide

  11. 1. Put the equation in standard from. Determine if the graph opens up or down and if it is normal, skinny, or wide. Standard Form: Opens down skinny

  12. 1. Put the equation in standard from. Determine if the graph opens up or down and if it is normal, skinny, or wide. Standard Form: Opens down normal

  13. 2. Identify the vertex. State the max or min. (2, –13) Vertex: ________________ y = –13 min/max value: _________

  14. 2. Identify the vertex. State the max or min. (1, 11) Vertex: ________________ y = 11 min/max value: _________

  15. 2. Identify the vertex. State the max or min. (0, 5) Vertex: ________________ y = 5 min/max value: _________

  16. 3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts.

  17. 3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. (2, 5) 2 (1, 8) 1 (0, 9) 0 –1 (–1, 8) –2 (–2, 5)

  18. (0, 9) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = 0 y = 9 3 or x - 3 = 0 x + 3 = 0 9 x = 3 x = -3

  19. (0, 9) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = 0 y = 9 3 9 (0, 9) (–1, 8) (–2, 5) (2, 5) (1, 8)

  20. 3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts.

  21. 3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. (4, 6) 4 (2, 0) 2 (0, –2) 0 –2 (–2, 0) –4 (–4, 6)

  22. (0, –2) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = 0 y = –2  2 –2

  23. (0, –2) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = 0 y = –2  2 –2 (4, 6) (2, 0) (0, –2) (–2, 0) (–4, 6)

  24. 3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts.

  25. 3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. (1, –9) 1 (0, 0) 0 (–1, 3) –1 –2 (–2, 0) –3 (–3, –9)

  26. (–1, 3) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = –1 -3x -3x -3x(x + 2) = 0 y = 3 or x + 2 = 0 -3x = 0 0, -2 x = -2 x = 0 0

  27. (–1, 3) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = –1 y = 3 0, -2 0 (1, –9) (0, 0) (–1, 3) (–3, –9) (–2, 0)

  28. 3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts.

  29. 3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. (0, 3) 0 (–1, 0) –1 (–2, –1) –2 –3 (–3, 0) –4 (–4, 3)

  30. (–2, –1) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = -2 x 3 x 1 y = –1 x 3x + -1, -3 (x + 3)(x + 1) = 0 3 x + 3 = 0 or x + 1 = 0 x = –3 x = –1

  31. (–2, –1) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = -2 y = –1 -1, -3 3 (0, 3) (–1, 0) (–2, –1) (–3, 0) (–4, 3)

  32. 3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts.

  33. 3. Sketch the graph of the quadratic equations. Identify the vertex, axis of symmetry, the minimum or maximum, the x­-intercepts, and the y-intercepts. (3, –8) 3 (2, –2) 2 (1, 0) 1 0 (0, –2) –1 (–1, –8)

  34. (1, 0) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ -2 -2 -2 x = 1 -2(x2 – 2x + 1) = 0 x -1 y = 0 x -1 1 -x -x + -2(x – 1)2 = 0 -2 (x – 1)2 = 0 x – 1 = 0 x = 1

  35. (1, 0) Vertex: ________________ axis of symmetry: ________ circle one: min or max min/max value: _________ x – intercept(s): _________ y-intercept: _____________ x = 1 y = 0 1 -2 (3, –8) (2, –2) (1, 0) (0, –2) (–1, –8)

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