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Systems of Equations

Inequalities
Equivalent Quadratics
Equivalent Quadratics
Important Features
100

y = 6x − 11

−2x − 3y = −7

( 2, 1)

100

2 q + 5 q > 154

q > 22

100

(x − 9)(x + 2)

x 2 − 7x − 18

100

p 2 − 5 p − 14

( p + 2)( p − 7)

100

Find the roots, vertex, and line of symmetry for:

f(x) = x2 + 3x + 2 

roots: (-2, 0) (-1, 0)

vertex: (-1.5, -0.25)

line of symmetry: x = -1.5

200

−4x + y = 6

−5x − y = 21

(-3, -6)

200

3 y - 6 + 4 y < 50

y < 8

200

(m − 1)(m − 8)

m 2 − 9m + 8

200

x 2 − 16x + 63

(x − 9)(x − 7)

200

Find the roots, vertex, and line of symmetry for:

f(x) = x2 - 4x - 45

roots: (9, 0)(-5, 0)

vertex: (2, -49)

line of symmetry: x = 2

300

−5x + y = −2

−3x + 6y = −12

(0, -2)

300

9 f - 200 > 2( 5 - 6 f)

f > 10

300

(7x + 4)(x − 5)

7x 2 − 31x − 20

300

7k 2 + 9k

k(7k + 9)

300

Find the roots, vertex, and line of symmetry for:

f(x) = 3x2 -15x + 18

roots: (2, 0) (3, 0)

vertex: (2.5, -0.75)

line of symmetry: x = 2.5

400

−14 = −20y − 7x

10y + 4 = 2x

(2, 0)

400

4 b - 239 > 5( 4 - 6 b) - 3 b

b > 7

400

(5p + 9)( p − 2)

5p 2 − p − 18

400

2b 2 + 17b + 21

(2b + 3)(b + 7)

400

Write 2 equations for the table below: 

x     -9     -8     -7      -6      -5     -4     -3     -2

f(x)   0     -6    -10    -12    -12    -10    -6     0

f(x) = x2 + 11x + 18

f(x) = (x + 9)(x + 2)


500

−3x + 3y = 4

−x + y = 3

No solution

500

3( 2 - 6 h) - 5 h > 7 h - 114

h < 4

500

b(3b − 2)(b − 1)

3b 3 − 5b 2 + 2b

500

9r 2 − 5r − 10

Not factorable

500

Write 2 equations for the table below: 

x     -2     -1     0      1      2 

f(x)   0     -3    -4    -3      0    

f(x) = x2 - 4

f(x) = (x + 2)(x - 2)