2.2.1 Graphing
Math 2
How do you graph the function (𝑥) = 𝑥 2 ?
What is the name for this type of function? ____________________________
What are some of the characteristics of the graph?
(Desmos Activity: https://www.desmos.com/calculator/ox4ejlfug7)
Practice:
1. y  ( x  1)2  2
2. y  2( x  2)2  5
Transformations: ________________
Transformations: ___________
Vertex: ____________
Vertex: ___________
A.O.S.: ____________
A.O.S.: ____________
Is the vertex a max or min?
Is the vertex a max or min?
2.2.1 Graphing
Math 2
3. y  3( x  7)2  8
4. y  ( x  5)2  3
Transformations: ______________
Transformations: ________________
Vertex = ____________
Vertex = __________
A.O.S. = ____________
A.O.S. = ____________
Is the vertex a max or min?
5. y  ( x  1)2  4
Transformations: _____________________
Is the vertex a max or min?
6. y  2( x  1)2
Transformations: _____________________
Vertex: ____________
Vertex: ___________
A.O.S.: ____________
A.O.S.: ____________
Is the vertex a max or min?
Is the vertex a max or min?
2.2.1 Graphing
Math 2
Write the equation of each parabola in vertex form.
7. _________________
8. _______________
9. _______________
Write the equation of each parabola in vertex form.
10. vertex (1,2), point (2,-5)
11. Vertex (-3,6), point (1,-2)
12. vertex (-1,-4), y-intercept: 3
9
1
13. Vertex  ,   , y-intercept: -1
 10 10 
Standard form of a quadratic:
How can you convert from vertex form to standard form?
Ex.) 𝑦 = −2(𝑥 − 1)2 + 4
Is there a way to find the vertex when it is written in standard form?
2.2.1 Graphing
Math 2
Practice: Find the vertex of each function and sketch the graph. Is the vertex and minimum or a maximum?
Where is the function increasing? Where is the function decreasing?
1. 𝑓(𝑥) = 2𝑥 2 − 4𝑥 + 6
2. 𝑦 = 𝑥 2 + 6𝑥 + 1
3. 𝑦 = −𝑥 2 + 5𝑥 − 1