1. Warm Up Identify the transformation for each function:
I can write an equation from a graph
Warm Up
Identify the transformation for each function:
a) 𝑦=−2 (𝑥+1) 3 −4 b) y= 𝑥+6 +2
c) 𝑥= (𝑦+3) 2 − d) (𝑥−1) 2 + 𝑦 2 =81
2. Write the equation of the cube root function that has an inflection point of (−7,1)

2. Warm Up Identify the transformation for each function:
−2 (𝑥+1) 3 − b) 𝑥+6 +2
c) 𝑥= (𝑦+3) 2 − d) (𝑥−1) 2 + 𝑦 2 =81

3. Warm Up
2. Write the equation of the cube root function that has an inflection point of (−7,1)

4. Homework Questions

5. Writing the equation of a function from a graph
Steps
Example
Identify the parent function
Identify ℎ,𝑘
Plug in ℎ,𝑘
Find a second point
𝑦= 𝑥 2
(−3,−4)
(−2,−2)
𝑦= 𝑎(𝑥−ℎ) 2 +𝑘
𝑦= 𝑎(𝑥−−3) 2 −4
𝑦= 𝑎(𝑥+3) 2 −4

6. Writing the equation of a function from a graph
Steps
Example
Find a second point
Plug in point and solve for a
Write final equation
𝑦= 𝑎(𝑥−ℎ) 2 +𝑘
(−2,−2)
𝑦= 𝑎(𝑥−−3) 2 −4
𝑦= 𝑎(𝑥+3) 2 −4
−2= 𝑎 − −4
−2= 𝑎 1 2 −4
−2=𝑎−4
2=𝑎
𝑦= 2(𝑥+3) 2 −4

7. Writing the equation of a function from a graph
Steps
Example
Identify the parent function
Identify ℎ,𝑘
Plug in ℎ,𝑘
Find a second point
𝑦= 𝑥
(0,−4)
(4,−3)
𝑦=𝑎 𝑥−ℎ +𝑘
𝑦=𝑎 𝑥−0 −4
𝑦=𝑎 𝑥 −4

8. Writing the equation of a function from a graph
Steps
Example
Find a second point
Plug in point and solve for a
Write final equation
𝑦=𝑎 𝑥−ℎ +𝑘
(4,−3)
𝑦=𝑎 𝑥−0 −4
𝑦=𝑎 𝑥 −4
−3=𝑎 4 −4
1=𝑎 4
1=2𝑎
𝑎= 1 2
𝑦= 𝑥 −4

9. Try this one…
Write the equation of the cube root function that has an inflection point at (3,−1) and goes through the point (−5,−5)

10. Writing Equations from Graphs WS
Homework
Writing Equations from Graphs WS