Ch. 5 Notecard Ideas
Linear Equation/Linear Function
- Linear graphs to a straight line
- Equation is = sign; function is f(x)
- Function- 1 “y” for every “x”
1. AKA- NOT a vertical line
X-intercept and Y-intercept
- Plug in 0 and solve
Slope
- Ryse/run
-
𝑦2−𝑦1
𝑥2−𝑥1
- Positive (up) /Negative (down)
- Zero (horizontal)/Undefined (vertical)
Slope-intercept Form
- 𝑦 = 𝑚𝑥 + 𝑏
ii. m= slope
iii. b= y-intercept
Point Slope Form
- 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)
How to graph from slope-intercept form
- Plot the y-intercept
- Start and y-int. and use slope
How to write an equation in slope-intercept form
from a graph
- Find y-intercept
- Find slope
- Plug into y=mx+b equation
Ch. 7 Note card Suggestions:
Break-even point:
- When the cost/expenses equal the income, or point
of intersection of the two lines.
Profit:
- Income minus expenses
Algebraically Verify a Solution:
- Plug in the point into both equations and check that
the solutions match.
Systems of Linear equations or Linear System:
1. Graphing:
a. Number of solutions
i. 1 solution: lines intersect
ii. Infinite: lines are the SAME
iii. 0 solutions: lines are PARALLEL
b. Parallel lines
i. Slopes are the same
c. Perpendicular
i. Slopes are OPPOSITES and RECIPROCALS
d. Neither
i. Slopes are NOT parallel or perpendicular
2. Substitution
a. Isolate a variable in one equation
b. Plug the expression into the variable that was
isolated in the 2nd equation
c. Solve for the variable.
d. Substitute the value into the 1st equation and
solve for the 2nd variable.
e. Write answer as an ordered pair (x, y)
f. Check your answer by plugging the numbers
into the equation.
3. Linear Combination/Elimination
a. Choose a variable to eliminate by adding
vertically.
b. Multiply 1 or 2 equations to make the numbers
opposites.
c. Add vertically.
d. Solve for the remaining variable.
e. Substitute the value into one equation and solve
for the other variable.
f. Write your answer as an ordered pair (x, y).
g. Check your answer by plugging the numbers
into the equation.
Graphing Linear Inequalities
1. Plotting points
a. Get the equation into Slope-intercept form
b. Plot the y-intercept
c. Use the slope to find the other points
2. Solid ( ≤, ≥) or Dashed (<, >)
3. Test which side to shade
a. Plug in (0,0)
4. Shade a side.
a. If 0 works- shade the side WITH 0 on it.
b. If 0 does NOT work- shade the side WITHOUT 0.
System of Inequalities
1. Graph both inequalities on one graph by using the
above steps.
Ch. 8 Note card Suggestions:
Quadratic Equation:
(Graph is a Parabola)
𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
Quadratic Formula:
𝑥=
−𝑏±√𝑏2 −4𝑎𝑐
2𝑎
Discriminant:
𝑏 2 − 4𝑎𝑐
+ = 2 solutions
-- = No solution
0 = 1 solution
Line of Symmetry:
(AKA- x-value of Vertex)
𝑏
𝑥=−
2𝑎
Vertex:
- Plug answer from Line of Sym. Into the “x” in the
equation and solve for “y”.
Vertical Motion Model:
𝑦 = −16𝑡 2 + 𝑣𝑡 + ℎ
T=time
V=initial velocity
H=initial height
Ch. 9 Note card Suggestions
List all factors= Factor pairs
Prime factorization= Factor tree
Product Rule of Exponents:
𝑎𝑏 ∙ 𝑎𝑐 = 𝑎𝑏+𝑐
EX: 35 ∙ 33 = 35+3 = 38
Quotient Rule of Exponents:
EX:
65
62
𝑎𝑏
𝑎𝑐
= 𝑎𝑏−𝑐
= 65−2 = 63
Zero Rule of Exponents:
𝑎0 = 1
EX: 20 = 1
Negative Exponent Rule: 𝑎 −𝑏 =
EX: 10
−3
=
1
10−3
Power of a Power Rule:
EX:
or
1
𝑎𝑏
1
103
= 10−3
𝑏 𝑐
(𝑎 ) = (𝑎𝑏∗𝑐 )
(32 )3 = (32∗3 ) = 36 = 64
Power of a Product Rule: (𝑎𝑏)𝑐 = (𝑎𝑐 )(𝑏 𝑐 )
(5𝑏)3 = (53 )(𝑏 3 ) = 125𝑏 3
EX:
b
𝑥3
𝑥3
4
4
64
𝑛
√𝑎 = 𝑎
Rational Exponent:
1
3
3
√7 = 7
3
2
b
𝑥 3
( ) = ( 3) =
EX:
ac
( ) = ( c)
Power of a Quotient Rule:
EX:
a c
x =x
1
∗3
2
1
𝑛
1
5
2
3
5
5
𝑚 = √𝑚
or
10
= ( √x) or ( √x)
=x
10
5
= x2
Scientific Notation:
EX: 410,000 = 4.1 ∗ 105 or 0.000052 = 5.2 ∗ 10−5
Standard Notation:
EX:1.8 ∗ 104 = 18,000
or 7.0 ∗ 10−4 = 0.0007
Ch. 10 Note card Suggestions:
Term and Coefficient:
EX:
10𝑎3 − 8𝑎 + 5
Terms: 10a^3, -8a, 5
Coefficients: 10, -8, 5
Classify by TERMS:
Monomial= 1 term
Binomial= 2 terms
Trinomial= 3 terms
Classify by DEGREE:
1st degree:
linear
(x)
2nd degree: Quadratic
3rd degree: Cubic
(𝑥 2 )
(𝑥^3)
Standard Form:
- Highest exponent to lowest Exponent: 𝑥 3 + 2𝑥 2 + 3
Add Polynomials:
- Combine LIKE terms
Subtract Polynomials:
- Distribute the (-) through the 2nd set of parenthesis.
- Combine LIKE terms
FOIL
(𝑥 + 6)(𝑥 + 3)
𝑥 2 + 3𝑥 + 6𝑥 + 18
𝑥 2 + 9𝑥 + 18
Difference of Two Squares (DTS):
𝑥 2 − 64 = (𝑥 + 8)(𝑥 − 8)
Perfect Square Trinomials (PST):
𝑥 2 + 12𝑥 + 36 = (𝑥 + 6)(𝑥 + 6) = (𝑥 + 6)2
Or
𝑥 2 − 12𝑥 + 36 = (𝑥 − 6)(𝑥 − 6) = (𝑥 − 6)2
Factor:
1. Look for GCF 1st.
2. Check terms
a. 2 terms- DTS?
b. 3 terms- factor
i. Box method (coefficient ≠1)
ii. Factor pairs for last term with S/D to middle
EX: 𝑥 2 + 5𝑥 + 6
Factor pairs for 6- 1&6; 2&3
Sum: 5 2&3
Set up parenthesis and find sign (middle term)
(x + 2) (x + 3)
Ch. 6 Notecard Ideas
Scatter Plot
- Know how to plot points
- Draw the “line of best fit”
- Create the equation of the “line of best fit”
o Find 2 points that are on or near the line.
o Use the slope formula
𝑦2−𝑦1
𝑥2−𝑥1
o Plug into point- slope formula m and 1 of
the points
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)