1. Math 3 final exam review Part 1
Unit 3: Linear Programming
Unit 3.2: Quadratic Functions
Unit 4: Higher-Order Polynomial Functions
Unit 7: Exponential & Log Functions
Math 3 final exam review Part 1

2. Unit 3: linear programming
Let x= and y= (define your variables)
Inequalities
Graph
cHart corner points
Tell your solution (full sentence)

3. Unit 3.2: Quadratic Functions
Standard Form:
𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐
Vertex Form:
𝑦=𝑎 (𝑥−ℎ) 2 +𝑘
(h, k) is the vertex
Domain: −∞, ∞
Range: [𝑘, ∞) if a>0
(−∞, 𝑘] if a<0

4. Unit 3.2: Quadratic Functions
𝑦= 𝑥 2 +2𝑥−8
Standard Form:
𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐
y-intercept: (0, y)
Plug in 0 for x
(it’s going to be the “c” value)
x-intercepts/roots: (x, 0), (x, 0)
Option 2:
𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎
Option 1:
𝐹𝑎𝑐𝑡𝑜𝑟, 𝑠𝑒𝑡 𝑒𝑎𝑐ℎ=0
Option 3:
𝑅𝑒𝑤𝑟𝑖𝑡𝑒 𝑖𝑛 𝑣𝑒𝑟𝑡𝑒𝑥
𝑓𝑜𝑟𝑚, 𝑠𝑜𝑙𝑣𝑒
vertex: (x, y)
Option 1:
𝑥= −𝑏 2𝑎 , 𝑡ℎ𝑒𝑛 𝑝𝑙𝑢𝑔
𝑖𝑛𝑡𝑜 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑡𝑜 𝑓𝑖𝑛𝑑 𝑦
Option 2:
𝑅𝑒𝑤𝑟𝑖𝑡𝑒 𝑖𝑛 𝑣𝑒𝑟𝑡𝑒𝑥 𝑓𝑜𝑟𝑚,
𝑣𝑒𝑟𝑡𝑒𝑥 𝑖𝑠 (ℎ,𝑘)

5. Unit 3.2: Quadratic Functions
𝑦= 𝑥 2 +2𝑥−8
Vertex Form:
𝑦=𝑎 (𝑥−ℎ) 2 +𝑘
y-intercept: (0, y)
Plug in 0 for x
x-intercepts/roots: (x, 0), (x, 0)
Plug in 0 for y, solve
(when you take the square root,
don’t for get ±‼‼‼)
vertex: (x, y)
Vertex is (h, k)

6. Unit 3.2: quadratic functions
Types of Roots:
𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎
Rational Roots:
Radicand is a perfect square:
Irrational Roots:
Radicand is NOT a perfect square:

7. Unit 3: Quadratic Functions
Convert Vertex Form to Standard Form
𝑦=2(𝑥−3 ) 2 +5
𝑦=2 𝑥−3 𝑥−3 +5
𝑦=2( 𝑥 2 −6𝑥+9)+5
𝑦=(2 𝑥 2 −12𝑥+18)+5
𝑦=2 𝑥 2 −12𝑥+23
Convert Standard Form to Vertex Form
𝑦=2 𝑥 2 −12𝑥+23
𝑦−23=2 𝑥 2 −12𝑥
𝑦−23 2 = 𝑥 2 −6𝑥
𝑦− = 𝑥 2 −6𝑥+9
𝑦− =(𝑥−3)(𝑥−3)
𝑦− = (𝑥−3) 2
𝑦−23 2 = (𝑥−3) 2 −9
𝑦−23= 2(𝑥−3) 2 −18
𝑦= 2(𝑥−3) 2 +5

8. Unit 3: Quadratic Functions
Focus & Directrix
𝑦= 1 4𝑝 (𝑥−ℎ ) 2 +𝑘
P is the distance from vertex to focus, will be negative if parabola opens down

9. Unit 4: Higher Order Polynomial Functions
End Behavior
Cubic, a>0
𝑎𝑠 𝑥→∞, 𝑦 𝑖𝑛𝑐
𝑎𝑠 𝑥→−∞, 𝑦 𝑑𝑒𝑐
Linear, m>0
𝑎𝑠 𝑥→∞, 𝑦 𝑖𝑛𝑐
𝑎𝑠 𝑥→−∞, 𝑦 𝑑𝑒𝑐
Cubic, a<0
𝑎𝑠 𝑥→∞, 𝑦 𝑑𝑒𝑐
𝑎𝑠 𝑥→−∞, 𝑦 𝑖𝑛𝑐
Linear, m<0
𝑎𝑠 𝑥→∞, 𝑦 𝑑𝑒𝑐
𝑎𝑠 𝑥→−∞, 𝑦 𝑖𝑛𝑐
Quadratic, a>0
𝑎𝑠 𝑥→∞, 𝑦 𝑖𝑛𝑐
𝑎𝑠 𝑥→−∞, 𝑦 𝑖𝑛𝑐
Quartic, a>0
𝑎𝑠 𝑥→∞, 𝑦 𝑖𝑛𝑐
𝑎𝑠 𝑥→−∞, 𝑦 𝑖𝑛𝑐
Quadratic, a<0
𝑎𝑠 𝑥→∞, 𝑦 𝑑𝑒𝑐
𝑎𝑠 𝑥→−∞, 𝑦 𝑑𝑒𝑐
Quartic, a<0
𝑎𝑠 𝑥→∞, 𝑦 𝑑𝑒𝑐
𝑎𝑠 𝑥→−∞, 𝑦 𝑑𝑒𝑐

10. Unit 4: Higher Order Polynomial functions
Solving when you can’t see all x-intercepts
1st Step: How many solutions?
Cubic (𝑥 3 ): 3 Quartic (𝑥 4 ): 4 Quintic (𝑥 5 ): 5

11. Unit 7: exponential & logarithmic functions
Growth:
𝑦=𝑎 𝑏 𝑥
b>1
Decay:
𝑦=𝑎 𝑏 𝑥
0<b<1
Exponential Functions
𝑦=𝑎 𝑏 𝑥−ℎ +𝑘
Growth/Decay Factor
Initial Amount
Domain: −∞, ∞
Range: 𝑘, ∞ if a>0
−∞, 𝑘 if a<0
All exponential functions have asymptotes at horizontal lines (e.g. y=0 for the graphs above, as the y values will never reach 0)

12. Unit 7: exponential & logarithmic functions
Exponential Evaluating
Rate: Percent/100
Growth:
𝑦=𝑎(1+𝑟 ) 𝑥
Decay:
𝑦=𝑎(1−𝑟 ) 𝑥
Rate: Percent/100
Compound Interest:
𝑦=𝑎(1+ 𝑟 𝑛 ) 𝑛𝑥
Number of times compounded per year
Compound Continuously:
𝐴=𝑃 𝑒 𝑟𝑡
Principle (same as “a”)
Amount in account at end (same as “y”)

13. Unit 7: exponential & logarithmic functions
Inverses: Reflections over y=x
Inverse Functions: Functions that “undo” one another through opposite operations.
For equations: Switch x and y, solve for y
For graphs: Reflect over line y=x
For points: Switch x and y

14. Unit 7: exponential & logarithmic functions
Composition of Functions

15. Unit 7: exponential & logarithmic functions
Composition of Functions with their Inverses

16. Unit 7: exponential & logarithmic functions
With Logarithms:
2( 5) 0.3𝑥 =30
( 5) 0.3𝑥 =15
log 5 (5 0.3𝑥 )= log 5 (15)
0.3𝑥= log⁡(15) log⁡(5)
𝑥=5.61
Exponential Solving
Without Logarithms:
Isolate base with exponent
Take log of both sides
Evaluate log 𝟓 𝟏𝟓
Solve

17. Unit 7: exponential & logarithmic functions
Logarithm Solving
Isolate logarithm
Exponentiate
Solve
Check for extraneous solutions