1. 8.1 Graphing f(x) = ax2

2. What we will learn Identify characteristics of quadratic functions
Graph and use quadratic functions of the form 𝑓 𝑥 =𝑎 𝑥 2

3. Needed vocab
Quadratic function: nonlinear function that can be written in the standard form 𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐
Parabola: u shaped graph
Vertex: highest or lowest point where parabola changes direction
Axis of symmetry: vertical line that divides parabola into two symmetric parts

4. Ex. 1 identifying characteristics
Identify vertex, axis of symmetry, domain, range, and behavior of the graph
Domain: all real numbers
Always
Range: 𝑥≥−2
Behavior on graph
Vertex on graph
Axis of symmetry on graph

5. Ex. 2 and 3 graphing 𝑦=𝑎 𝑥 2 Core concept:
When comparing to parent of 𝑦= 𝑥 2
If a is between 0 and 1, then wider
If a is greater than 1 or less than -1, then skinnier

6. Ex. 2 and 3 Continued Make a table Show 3 out of 5 x’s Plot the points
Graph 𝑦=2 𝑥 2
𝑦=2 −2 2
𝑦=2(4)
𝑦=8 X Y -2 8 -1 2 1

7. Ex. 4 story problems
The diagram shows the cross section of a satellite dish, where x and y are measured in meters. Find the width and depth of the satellite.
Just read graph
Y is depth, and X is width
Width is 4 meters
Depth is 1 meter