1. Using the Vertex Form of Quadratic Equations

2. Vertex Form of Quadratic Equations
f(x) = a(x – h)2 + k
vertex; (h, k)

3. Example 1 Given an equation: y = (x + 4)2 – 9 Determine:Up
1. How it opens
(- 4, -9)
y = (x - - 4)2 + – 9
2. vertex
3. axis of symmetry
x = -4
4. minimum/maximum point
---- minimum at -9
5. y-intercept
6. y-intercept reflection
7. roots

4. Example 1 y = (x + 4)2 – 9 (0,7) 5. y-intercept y = (0 + 4)2 – 9
6. y-intercept reflection
(-8,7)
x = -1 and x = -7
7. Roots
vertex: (-4, 9)
y = (x + 4)2 – 9
x + 4 = 3 and x + 4 = - 3
x = - 1 and x = -7
0 = (x + 4)2 – 9
9 = (x + 4)2
+/- 3 = x + 4

5. Example 2 Given an equation: y = (x - 2)2 + 4 Determine:Up
1. How it opens
( 2, 4)
2. vertex
3. axis of symmetry
x = 2
4. minimum/maximum point
---- minimum at 4
5. y-intercept
6. y-intercept reflection
7. roots

6. Example 2 y = (x - 2)2 + 4 (0,8) 5. y-intercept y = (0 - 2)2 + 4
6. y-intercept reflection
(4,8)
no roots
7. Roots
vertex: (2, 4)
y = (x - 2)2 + 4
0 = (x - 2)2 + 4
- 4 = (x - 2)2

7. Example 3 Given an equation: y = (x + 2)2 – 3 Determine:Up
1. How it opens
(- 2, -3)
y = (x - - 2)2 + – 3
2. vertex
3. axis of symmetry
x = -2
4. minimum/maximum point
---- minimum at -3
5. y-intercept
6. y-intercept reflection
7. roots

8. Example 3 y = (x + 2)2 – 3 (0,1) 5. y-intercept y = (0 + 2)2 – 3
6. y-intercept reflection
(- 4,1)
x = and x =
7. Roots
vertex: (-2, - 3)
y = (x + 2)2 – 3
x + 2 =__ and x + 2 = - __
x = ___ and x = ___
0 = (x + 2)2 – 3
3 = (x + 2)2
_____ = x + 2

9. Example 4 Given an equation: y = 2(x - 3)2 – 8 Determine:Up
1. How it opens
(3, -8)
y = 2(x - 3)2 + – 8
2. vertex
3. axis of symmetry
x = 3
4. minimum/maximum point
---- minimum at -8
5. y-intercept
6. y-intercept reflection
7. roots

10. Example 4 y = 2(x - 3)2 – 8 (0,10) 5. y-intercept y = 2(0 - 3)2 – 8
6. y-intercept reflection
(6,10)
x = 1 and x = 5
7. Roots
vertex: (3, - 8)
y = 2(x - 3)2 – 8
x - 3 = 2 and x - 3 = - 2
x = 5 and x = 1
0 = 2(x - 3)2 – 8
8 = 2(x - 3)2
4 = (x – 3)2