Remediation 2.1 CFA Key Features

downward

upward

upward

downward

(3,0) and (8,0)

(-3,0) and (-8, 0)

(-3, 0) and (8,0)

(3, 0) and (-8, 0)

(3, 0) and (-2, 0)

(-6, 0) and (4, 0)

(6, 0) and (-4, 0)

(-6, 0) and (-4, 0)

(5,0) & (1,0)

(5,0) & (-1,0)

(-5,0) & (1,0)

(-5,0) & (-1,0)

(x+5)(x-7)=0

(x-5)(x+7)=0

(x+5)(x+7)=0

(x-5)(x-7)=0

roots

vertex

solutions

x intercepts

y = (x-2)(x-5)

y = (x+2)(x+5)

y = -(x+2)(x+5)

y = -(x-2)(x-5)

$$\left(-\infty,\infty\right)$$

(- $$\infty$$ , 0)

To infinity and beyond

(0, $$\infty$$ )

$$\left(-4,\infty\right)$$  

All Real Numbers

$$\left(-3,\infty\right)$$

$$\left(-\infty,\ 4\right)_{ }$$  

All real numbers

$$\left[4,\infty\right)$$

$$\left(-\infty,4\right]$$

$$\left(-\infty,1\right]$$

$$\left[-4,\infty\right)$$  

$$\left(-\infty,\infty\right)$$

$$\left[-3,\infty\right)$$  

$$\left(-\infty,4\right]$$  

Domain: $$\left(-6,2\right)$$

Range: $$\left(-3,5\right)$$

Domain: $$\left(-\infty,\infty\right)$$

Range: (-3,5)

Domain: $$\left(-\infty,\infty\right)$$

Range: $$\left[-3,\infty\right)$$

Domain: $$\left(-\infty,\infty\right)$$

Range: $$\left(-\infty,-3\right]$$

Domain : (-2,2)
Range : (0,4)

Domain : (0,4)
Range : (-2,2)

Domain : $$\left(-\infty,\infty\right)$$
Range : $$\left(-\infty,4\right]$$

Domain : $$\left(-\infty,\infty\right)$$
Range : $$\left[4,\infty\right)$$

(0, 1)

(2, 1)

(0, 3)

(0, -3)

a vertical line

a horizontal line

x = 1

x = 0

(2, 4)

(3, -1)

(4, 2)

(0, 8)

Vertex: (8, 3); axis of symmetry: y=3

Vertex: (8, 3); axis of symmetry: x=3

Vertex: (3, 8); axis of symmetry: y=3

Vertex: (3, 8); axis of symmetry: x=3

Maximum

Minimum

Neither

Both

(-1,0)

(1,-4)

(0,-3)

(3,0)

(4,-1)