5.1 Graphing Quadratic Functions
- 2. What is a Quadratic Function? A function with the form y = ax2 + bx + c where a 0. The graph is U-shaped and is called a parabola.
- 3. Why Study Quadratics? Many things we see every day are modeled by quadratic functions. What are some examples? ◦ Water in a drinking fountain ◦ The McDonald’s Golden Arches ◦ The path of a basketball
- 4. Quadratic Vocab The lowest or highest point is called the vertex. The axis of symmetry is a vertical line through the vertex.
- 5. Effects of “a” Standard Form: y = ax2 + bx + c Just like with absolute value functions: ◦ If a > 0 (+), the parabola opens up ◦ If a < 0 (-), the parabola opens down ◦ If |a| < 1, the parabola is wider than y = x2 ◦ If |a| > 1, the parabola is narrower than y = x2
- 6. Finding the Vertex The x-coordinate of the vertex is To find the y, plug in the x-coordinate. Example: Find the vertex. y = 2x2 – 8x + 6 Axis of symmetry is the line x =
- 7. Graphing in Standard Form Find and plot the vertex. Example: Draw the axis of y = 2x2 – 8x + 6 symmetry. Choose two x values on one side and plot the points. Use symmetry to plot two points on the other side. Connect the points with a curve (parabola).
- 8. Example: Graph y = -x2 + 4x - 2
- 9. Your Turn! Graph
- 10. Vertex Form y = a(x – h)2 + k The vertex is (h, k) Axis of symmetry is x = h. Just like absolute value functions: ◦ h shifts right or left ◦ k shifts up or down ◦ a determines direction and width
- 11. Graphing in Vertex Form Same steps as for Standard Form. Example: Graph
- 12. Example: Graph
- 13. Your Turn! Graph
- 14. Intercept Form y = a(x – p)(x – q) X-intercepts are p and q Axis of symmetry is halfway between (p, 0) and (q, 0).
- 15. Graphing in Intercept Form Plot the intercepts: (p, 0) and (q, 0) Example: y = -(x + 2)(x – 4) The x-coordinate of the vertex is in the middle of the x-intercepts. Plug it in to find y, then plot the vertex. Connect the 3 points with a curve (parabola).
- 16. Example: Graph
- 17. Your Turn! Graph
- 18. Writing in Standard Form Multiply! (Use FOIL) Example: Write in standard form:
- 19. Example: Write in standard form:
- 20. Your Turn! Write in standard form: 1. 2.