1. Quiz 4 – 8 1. Solve using the quadratic formula: 2. Use the descriminant ( ) to determine if there are to determine if there are 0, 1, or 2 real roots. 0, 1, or 2 real roots.

2. 4 – 10 Write Quadratic Functions and Models

3. Vertex Form and Intercept Form Remember: A function is a rule that relates input values (x) to output values (y). input values (x) to output values (y). 1. Your turn: a = ? h = ? k = ? 2. a = ? h = ? k = ? 2. a = ? h = ? k = ? 3. a = ? h = ? k = ? 3. a = ? h = ? k = ? 4. a = ? p = ? q = ? 5. a = ? p = ? q = ? 5. a = ? p = ? q = ? 6. a = ? p = ? q = ? 6. a = ? p = ? q = ?

4. Today We are going to write the quadratic equation just by looking at the graph. just by looking at the graph. You’ll get: (1) A graph (2) a point on the graph (3) either the vertex or the two x-intercepts

5. Vertex Form Vertex: (h, k) = (4, 2) Point: (x, y) = (2, 6) (1) Did they give x-intercepts or the vertex? (2) Vertex  write the general vertex form quadratic eq. (3) Plug given values into the equation. 6422 (4) Solve for “a”. (5) Write the specific vertex form equation for this graph.

6. Vertex Form Vertex: (-3, -1) Point: (x, y) = (-5, -9) (1) Did they give x-intercepts or the vertex? (2) Vertex  write the general vertex form quadratic eq. (3) Plug given values into the equation. -9-3-5 (4) Solve for “a”. (5) Write the specific vertex form equation for this graph.

7. Your turn: 7. Find the equation Vertex: (-4, -2) Point: (x, y) = (-3, 0) (1) Did they give x-intercepts or the vertex? (2) Vertex  write the general vertex form quadratic eq. (3) Plug given values into the equation. 0-4-3-2 (4) Solve for “a”. (5) Write the specific vertex form equation for this graph.

8. Your turn: 8. Find the equation Vertex: (3, -1) Point: (x, y) = (2, -4) (1) Did they give x-intercepts or the vertex? (2) Vertex  write the general vertex form quadratic eq. (3) Plug given values into the equation. -432 (4) Solve for “a”. (5) Write the specific vertex form equation for this graph.

9. Intercept Form x-intercepts: 4, 1 x-intercepts: 4, 1 Point: (x, y) = (3, -4) (1) Did they give x-intercepts or the vertex? (2) x-intercepts  write the general intercept form quadratic eq. (3) Plug given values into the equation. -4431 (4) Solve for “a”. (5) Write the specific intercept form equation for this graph. 3

10. x-intercepts: -2, -4 x-intercepts: -2, -4 Point: (x, y) = (-5, -9) (1) Did they give x-intercepts or the vertex? (2) x-intercepts  write the general intercept form quadratic eq. (3) Plug given values into the equation. -9-2-5-4 (4) Solve for “a”. (5) Write the specific intercept form equation for this graph. -5 Your turn: 9. Find the equation

11. (1) Did they give x-intercepts or the vertex? (2) Both  write the general intercept form quadratic eq. (3) Plug given values into the equation. -4246 (4) Solve for “a”. (5) Write the specific intercept form equation for this graph. 4 Your turn: 10. Find the equation in intercept form. in intercept form. (2, 0) (6, 0) (4, -4)

12. What if: They wanted the final equation in standard form? (1) Find either vertex or intercept form (depending on whether they gave a vertex or intercepts. on whether they gave a vertex or intercepts. (2) Simplify (multiply and combine like terms) to convert to standard form. convert to standard form.

13. Your turn: Convert the following equations to standard form. 11. 12. 13. 13.

14. Your Turn: 14.15.16. Find the slope of the right side and vertex of each graph.

15. Your turn: y = f(x + 3) – 4 y = f(x + 3) – 4 (0, 0) x - 3 (-3, 0) y – 4 (-3, -4) stretch shift shift 28. f(x): (0, 0) (2, 3) 2 + 12 + 12 + 12 + 1 (3, 3) 3 + 2 (3, 5) Apply the given transformation to the point. 29. g(x): (2, 3) y = f(x – 1) + 2 y = f(x – 1) + 2