1. Quadratic Functions Unit Objectives: Solve a quadratic equation.
Graph/Transform quadratic functions with/without a calculator
Identify function attributes: domain, range, vertex, line of symmetry, number and nature of roots, maximum/minimum values.
Model situations with quadratic functions.
Today’s Objective:
Identify attributes and graph quadratic functions

3. Quadratic Function: 𝑓 𝑥 =𝑎 𝑥 2 +𝑏𝑥+𝑐, where 𝑎≠0 𝑦= 𝑥 2 Graph:
Parabola
Parent function/equation:
Vertex
Point where graph changes direction
Minimum or maximum
Vertex Form: 𝑦=±𝑎 (𝑥−ℎ) 2 +𝑘
Vertex: (h, k)
Axis of Symmetry (line)
Divides the graph into 2 mirror images
x = h

4. Transformation of 𝑓 𝑥 = 𝑥 2
Translation: Vertical
Translation: Horizontal
Up k units
Right h units
𝑦= 𝑥 2 +𝑘
𝑦= (𝑥−ℎ) 2
Down k units
Left h units
𝑦= 𝑥 2 −𝑘
𝑦= (𝑥+ℎ) 2
Reflection
Dilation:
𝑦=𝑎 𝑥 2
Stretch:
Across x-axis
𝑦=− 𝑥 2
𝑎>1
Vertex Form:
𝑦=±𝑎( 𝑥−ℎ) 2 +𝑘
Compression:
0<𝑎<1

5. Graphing a Quadratic Function in vertex form
𝑦= (𝑥−3) 2 +2
Vertex:
(3, 2)
Plot the vertex
Find and plot two points to the right of vertex.
Plot the point across axis of symmetry.
Sketch the curve.
Units right of vertex x
Units up from vertex 1 2
𝑥 2 1
Axis of Symmetry:
Domain:
Range: 4
𝑥=3
3 key-points
All Real Numbers
𝑦≥2

6. Graphing a Quadratic Function in vertex form
𝑦= 2𝑥 2
Vertex:
(0, 0)
Plot the vertex
Find and plot two points to the right of vertex.
Plot the point across axis of symmetry.
Sketch the curve.
Units right of vertex x
Units up from vertex 1 2
2𝑥 2 2
Axis of Symmetry:
Domain:
Range:
𝑥=0 8
3 key-points
All Real Numbers
𝑦≥0

7. Graphing a Quadratic Function in vertex form
𝑦= − (𝑥+4) 2 −3
Vertex:
(−4, −3)
Plot the vertex
Find and plot two points to the right of vertex.
Plot the point across axis of symmetry.
Sketch the curve.
Units right of vertex x
Units up from vertex 1 2
− 𝑥 2
− 1 2
Axis of Symmetry:
Domain:
Range: −2
𝑥=−4
All Real Numbers
𝑦≤−3

8. Writing a Quadratic function: vertex form 𝑦=±𝑎 (𝑥−ℎ) 2 +𝑘
Identify the Vertex:
(−2, −7)
𝑦=𝑎 (𝑥+2) 2 −7
Finding dilation factor:
Choose another known point and solve for a.
−5=𝑎 (−1+2) 2 −7
(-1, -5)
2=𝑎
𝑦=2 (𝑥+2) 2 −7
(-2, -7)

9. Writing a Quadratic function: vertex form 𝑦=±𝑎 (𝑥−ℎ) 2 +𝑘
(3, 9)
Identify the Vertex:
(3, 9)
𝑦=𝑎 (𝑥−3) 2 +9
(5, 7)
Finding dilation factor:
Choose another known point and solve for a.
7=𝑎 (5−3) 2 +9
−2=4𝑎
Practice W.S.: Graphing Quadratic Functions in Vertex Form
− =𝑎
𝑦= − (𝑥−3) 2 +9