1. Y= a ( x - h )2 + k Algebra 2: Notes 4.1 & 4.2: Pg.236 Pg.245 Pg.246
Graph Quadratic Functions in Standard, Vertex, or Intercept Form.
GOALS: “”
Pg.236
Pg.245
Pg.246
Quadratic Function:
Minimum Value:
Parabola:
Pg.238
Vertex:
Maximum Value:
Axis of Symmetry:
Vertex Form:
Intercept Form:
The Forms: Vertex Form
Y= a ( x - h )2 + k
Example 1: Can we multiply? If so give dimensions of the answer.
a>0 opens up
a<0 opens down
|a|>1 narrow
0<|a|<1 wide
If x-5 then h=+5
If x+5 then h=-5
h is the x value of the vertex.
If +6 then k=6
If -6 then k=-6
k is the y value of the vertex.

2. Y= ax2 + bx + c Y= a (x - p) (x - q)
Alg. 2 Notes: The Forms: Standard Form
Y= ax2 + bx + c
Use to find x value of vertex.
Plug in for x and find y to get y value of the vertex.
a>0 opens up
a<0 opens down
|a|>1 narrow
0<|a|<1 wide
(0,c) is the y -intercept.
The Forms: Intercept Form
Y= a (x p) (x - q)
Example 1: Can we multiply? If so give dimensions of the answer.
a>0 opens up
a<0 opens down
|a|>1 narrow
0<|a|<1 wide
(p,0) and (q,0) are the x-intercepts.
x-value of the vertex is (p+q)/2
y-value of vertex, plug in x and find y.

3. y = -2x2+2 b. y= -x2+4x-3 c. y= ½ (x+1)2 - 2 d. y= -2(x - 1)(x - 5)
(4.1 & 4.2) Example 1: Graph. Label the vertex, axis of symmetry, and x-intercepts. Compare each to y=x2. Does it have a maximum or a minimum?
y = -2x2+2
b. y= -x2+4x-3
c. y= ½ (x+1)2 - 2
d. y= -2(x - 1)(x - 5)

4. Example 1 (d). y= -2(x - 1)(x - 5)
(4.1 & 4.2) Example 2: Change (c) and (d) from example 1 into standard form.
Example 1(c). y= ½ (x+1)2 - 2
Example 1 (d). y= -2(x - 1)(x - 5)
FOIL METHOD
Words: To multiply two expressions that each contain two terms, add the
products of the First terms, the Outer terms, the Inner terms and the Last terms.
Example F O I L
(x + 4)(x + 7) = x2 + 7x + 4x + 28 = x2 + 11x + 28

5. y = -2x2+2 b. y= -x2+4x-3 d. y= -2(x - 1)(x - 5) c. y= ½ (x+1)2 - 2
(4.1 & 4.2) Example 1: (answers)
y = -2x2+2
b. y= -x2+4x-3
Maximum: (2,1)
Axis of symmetry: x=2
x-intercepts: (1,0) & (3,0)
Opens down, same width, vertex shifted right 2 units and up 1 unit.
Maximum: (0,2)
Axis of symmetry: x=0
x-intercepts: (-1,0) & (1,0)
Opens down, narrower, vertex shifted up 2 units.
d. y= -2(x - 1)(x - 5)
c. y= ½ (x+1)2 - 2
Maximum: (3,8)
Axis of symmetry: x=3
x-intercepts: (1,0) & (5,0)
Opens down, narrower, vertex shifted right 3 units and up 8 units.
Minimum: (-1,-2)
Axis of symmetry: x=-1
x-intercepts: (-3,0) & (1,0)
Opens up, wider, vertex shifted left 1 unit and down 2 units.
(4.1 & 4.2) Example 2: (answers)
d. y=-2x2 + 12x – 10
c. y= ½x2 + x – 3/2