Where
Ch. 2
How to
Simplify
What to do
Distribute (×)
Combine (+ or - ) like terms
IE) −3𝑥 − (2𝑥 − 4) + 6𝑥 − 9
Ch. 3
Solve
IE) 𝑥 2 − (𝑥 − 3𝑥 2 ) + 5
Undo what has been done to the variable that
is being isolated, by:
+/×/÷
IE) −2𝑥 + 4 = −6
IE) −3 = 12𝑦 − 5(2𝑦 − 7)
IE) 2𝑥 − 3𝑦 − 4𝑧 = 8 (solve for z)
Ch.4
Linear
Parent Linear Function
Equations
Ch.4
Find
Slope (m)
𝑦=𝑥
𝑟𝑖𝑠𝑒
𝑦2−𝑦1
𝑟𝑢𝑛
𝑥2−𝑥1
(−3,2) and
(−1, −2)
Ch. 4
Graph
use 𝑦 = 𝑚𝑥 + 𝑏 (slope –intercept form)
a line
m= slope
b= y-intercept
IE)
– 𝟑𝒙 − 𝟐𝒚 = −𝟖
a) use 𝑦 = 𝑚𝑥 + 𝑏
change from standard form
to slope intercept
b) make a table
x
c)find intercepts(always 0)
y
x-intercept
(
Ch.5
Write
y-intercept
,0)
(0,
)
use 𝑦 = 𝑚𝑥 + 𝑏 (slope –intercept form)
linear
eq.
m= slope
b= y-intercept
IE)
IE) (−6,2)and(−1, −3)
m=
b=
Ch.6
Solve
IE) −2𝑥 + 6 < −4
IE)4𝑥 − 𝑦 < −2
IE) −3 < 1 − 2𝑥 ≤ 3
IE)5𝑥 − 6 < −16 𝑜𝑟 − 13𝑥 ≤ 39
𝑥−𝑦 <1
4𝑥 + 2𝑦 ≤ −6
Ch.7
Solve a
System
By Graphing
By Substituion
10𝑥 + 5𝑦 = 5
−𝑥 + 3𝑦 = −9
2𝑥 − 3𝑦 = −3
8𝑥 − 4𝑦 = 32
By Elimination
3𝑥 + 4𝑦 = 10
7𝑥 − 4𝑦 = −30
Ch.8
Simplify
Exponents
Add/Subtract (must be like terms)
Coefficients: +/−
Exponent: stay same
IE) 𝑥 − 𝑥
IE) 𝑥 + 𝑥 2 − 3𝑥 IE) −2𝑥 − 3𝑦 − 3𝑥 + 2𝑦
Multiply Expressions (multiply anything)
Coefficients :∗(multiply)
Exponents: add exponents
IE)𝑥(−𝑥) IE) 𝑥 (𝑥 2 )(−3𝑥) IE)−2𝑥 (−3𝑦)(−3𝑥)(2𝑦)
Divide Expressions (divide anything)
Coefficients:
∗
(Multiply)
Exponents: subtract exponents
IE)
𝑥3
𝑥2
IE)
−4𝑥 6 𝑦 3 𝑧
2𝑥 2 𝑦
IE)
−5𝑎3 𝑏5 𝑐 4 𝑑 6
25𝑎5 𝑏5 𝑐 2 𝑑 10
Product to a Power
Coefficient: raise to the exponent
Exponents: multiply
IE) (2𝑥𝑦 5 )3
IE)(−3𝑥 2 )4
−2𝑚6
IE)(
3𝑛4
)
Negative Exponent
Flips the base to numerator or denominator
IE)
Ch.9
Simplify
−2
𝑥 −3
IE)
−6𝑦 −3 𝑧
IE)(−4𝑥 −3 𝑦 2 𝑧 −1 )
𝑥 −2
*get rid of (parenthesis): Distribute then
Combine like terms
Polynomials
IE) (8𝑐 2 − 4𝑐 + 1) + (−3𝑐 2 + 𝑐 − 5)
IE) (3𝑚 + 4) − (2𝑚2 − 6𝑚 + 5)
IE)𝑥(−𝑥 2 − 4𝑥 − 1)
IE)−5𝑎2 (4𝑎3 − 1)
IE) (3𝑥 2 )(−2𝑥 4 ) − (−5𝑥)(𝑥 5 ) − 𝑥 5
FOIL
IE)(𝑥 + 2)(𝑥 − 8)
IE) (7𝑎 − 6)
IE)(2𝑥 − 5)(3𝑥 − 4)
IE) (7𝑎 − 6)(7𝑎 + 6)
Ch.9
Factor
try to figure out what multiplies to make
the product
Factor
Ch.10
Quadratics
Graph
Product
2∗3
6
2𝑥 (𝑥 − 1)
2𝑥 2 − 2𝑥
(𝑥 + 1)(𝑥 + 4)
𝑥 2 + 5𝑥 + 4
(2𝑥 − 3)(3𝑥 − 4)
6𝑥 2 − 17𝑥 + 12
IE)𝑚2 − 10𝑚 + 24
IE)5𝑥 2 + 25
IE) 4𝑥 2 + 2𝑥 − 2
IE)6𝑐 2 + 7𝑐 + 2
Quadratics –Standard Form: 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0
𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 𝑦
Parabola
Parent Function/Graph
𝑦 = 𝑥2
To Graph
𝑦 = 2𝑥 2 − 11𝑥 + 5
Find Vertex: 𝑥 =
−𝑏
2𝑎
Find y-int: c value
(0, )
Find x- int:(
,0)( ,0)
Ch. 10
Solve
Quadratics
Solve 0 = 2𝑥 2 − 11𝑥 + 5
Methods
1. X-intercept (zero’s)(roots)
2. Factoring
3. Quadratic Formula
−𝑏±√𝑏2 −4𝑎𝑐
2𝑎
Solve 𝑦 = 2𝑥 2 − 11𝑥 + 5
1. By graphing and finding the x-intercepts –
wherever the graph hits the axis is also
the solution (usually 2, sometimes only 1,
and if none then there is no solution)
Solve 𝑦 = 2𝑥 2 − 11𝑥 + 5
( ,0)( .0)
Graph the equation in the calculator
and look for the x-intercepts
Solve 0 = 2𝑥 2 − 11𝑥 + 5
2. By Factoring
Solve 0 = 2𝑥 2 − 11𝑥 + 5
(
)(
)
Then set each factor equal to 0 and solve
3. Quadratic Formula
Solve
0 = 2𝑥 2 − 11𝑥 + 5
−𝑏±√𝑏2 −4𝑎𝑐
2𝑎
Other Information
Parallel lines - ________________ Perpendicular Lines_____________________
Parent Functions
Linear: 𝑦 = 𝑥
Quadratic: 𝑦 = 𝑥 2
Domain:
Functions:
Range:
Function Notation:
Scale Factors:
Similar Figures:
Direct Variation:
Percents
Probability: