1. Homework Questions

2. Vertex Form and Graphing Quadratics

3. Vertex Form of a Quadratic Equation
y = a (x - h)2 + k vertex (h, k)
Write the equation in vertex form.
Ex: y = x2 - 4x + 4

4. Write the equations in vertex form:
1. y = x2 + 6x y = -3x2 – 12x - 8

5. Try: Write in vertex form
1. y = 2x x + 19

6. Convert to Standard Form
y = (x+3)2 - 1
y = -3(x -2 )2 +4

7. Properties for graphing a Quadratic:
The graph of y = a(x – h)2 + k is the graph of
y = ax2 translated h units horizontally and k units vertically.
when h > 0 the graph shifts right;
when h < 0 the graph shifts left.
when k > 0 the graph shifts up;
when the k < 0 the graph shifts down.
the vertex is (h, k)
the axis of symmetry is the line x=h.

8. Example 1: Using Vertex Form to Graph a Parabola2
Graph y = - (x-2)2 +3
Vertex ( , )
Translation:
AOS x =
Max or Min at

9. Using Vertex Form to Graph a Parabola
Graph y = 2 (x+1)2 - 4
1. Vertex ( , )
2. Translation:
3. AOS x =
4. Max or Min at

10. Find the vertex from standard form w/o calculator:
Ex: x² -2x -3
x = then, y = plug x in equation
AOS is x = x coordinate of vertex
y intercept is (0,c)
Maximum or Minimum is same as vertex.

11. Try: -x² + 4x + 2 Find the following: Vertex ( , ) AOS x =
y intercept is ( , )
Max or Min ( , )

12. Try: Find the following: Vertex ( , ) AOS x = y intercept is ( , )
Max or Min ( , )

13. Find Vertex and Maximum or Minimum using a Calculator
Ex: y = 3x² + 12x +8

14. FINALLY - Using the Calculator to find x-intercepts
Solve:
1.  Set y= and graph with a standard window.
2.  Also set y = 0 in y2
3.  2nd Trace the intersection of your two “curves” aka y1 and y2

15. Using a Graphing Calculator Solve Each Equation (find x-int)
x2 + 6x + 4 = 0
3x2 + 5x - 12 = 8

16. Homework
Write this on the top of your homework paper so you will remember what to do!
Print out tomorrows PowerPoint so you don’t have to copy down word problems!
On your homework sheet you need to do the following for each problem:
Vertex
AOS
Any and all x-intercepts