Embed Size (px)
Citation preview
1
Notes 21 Using Transformations to Graph Quadratic Functions
Objectives:
Transform quadratic functions
Describe the effects of changes in the coefficients of y = a(x h)2 + k
Why learn this?
You can use transformations of quadratic functions to analyze changes in braking distance.
2
A quadratic function is a function that can be written in the form
The Ushaped curve that of a quadratic is called a parabola.
3
Graphing Quadratic Functions using a Table
Ex. Graph by using a table.
Find the xvalue of the vertex (when in standard form use )
Place this value in the middle of your table. Pick two values less than this number and two values greater.
Plot your points.
4
Try these:
Ex. Graph by using a table.
5
Ex. Using the graph of f(x) = x2 as a guide, describe the transformations, and then graph each function.
a.
b.
6
7
Try these:
Ex. Using the graph of f(x) = x2 as a guide, describe the transformations, and then graph each function.
a.
b.
8
9
Ex. Using the graph of f(x) = x2 as a guide, describe the transformations, and then graph each function.
a.
b.
10
Try these:
Ex. Using the graph of f(x) = x2 as a guide, describe the transformations, and then graph each function.
a.
b.
11
If a parabola opens upward, it has a lowest point. If a parabola opens downward, it has a highest point. This lowest or highest point is the vertex of a parabola
Vertex form:
Coordinates of vertex in vertex form: (h, k)
12
Ex. Use the description to write to write the quadratic function in vertex form.
The parent function f(x) = x2 is reflected across the xaxis, vertically stretched by a factor of 6, and translated 3 units left to create g.
Identify how each transformation affects a, h, and k.
Write the transformed function.
13
Try these:
Ex. Use the description to write the quadratic function in vertex form.
a. The parent function f(x) = x2 is vertically compressed by a factor of and translated 2 units right and 4 units down to create g.
b. The parent function f(x) = x2 is reflected across the xaxis and translated 5 units left and 1 unit up to create g.
