8.1 Graphing f(x) = ax2

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

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

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

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

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

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