This document discusses quadratic functions and transformations. It defines key terms like parabola, vertex, and axis of symmetry. It explains how the a value in the vertex form y=a(x-h)^2+k determines if a parabola is vertically stretched or compressed. It also states that if a is negative, the graph is reflected over the x-axis. The minimum or maximum value of a quadratic is always the y-coordinate of the vertex. The document provides examples of graphing and writing quadratic functions using vertex form.
1. CHAPTER 4 QUADRATIC FUNCTIONS
AND EQUATIONS
4.1 Quadratic Functions and Transformations
2. DEFINITIONS
A parabola is the graph of a quadratic function.
A parabola is a “U” shaped graph
The parent Quadratic Function is
3. DEFINITIONS
The vertex form of a quadratic function makes it
easy to identify the transformations
The axis of symmetry is a line that divides the
parabola into two mirror images (x = h)
The vertex of the parabola is (h, k) and it
represents the intersection of the parabola and the
axis of symmetry.
4. REFLECTION, STRETCH, AND COMPRESSION
Working with functions of the form
The determines the “width” of the parabola
If the the graph is vertically stretched (makes the “U”
narrow)
If the graph is vertically compressed (makes
the “U” wide)
If a is negative, the graph is reflected over the x–
axis
5. MINIMUM AND MAXIMUM VALUES
The minimum value of a function is the least y –
value of the function; it is the y – coordinate of the
lowest point on the graph.
The maximum value of a function is the greatest
y – value of the function; it is the y – coordinate of
the highest point on the graph.
For quadratic functions the minimum or maximum
point is always the vertex, thus the minimum or
maximum value is always the y – coordinate
of the vertex
7. TRANSFORMATIONS – USING VERTEX FORM
Graphing Quadratic Functions:
1. Identify and Plot the vertex and axis of symmetry
2. Set up a Table of Values. Choose x – values to the
right and left of the vertex and find the
corresponding y – values
Note: a is NOT slope
3. Plot the points and sketch the parabola
12. TRANSFORMATIONS – USING VERTEX FORM
Writing the equations of Quadratic Functions:
1. Identify the vertex (h, k)
2. Choose another point on the graph (x, y)
3. Plug h, k, x, and y into and
solve for a
4. Use h, k, and a to write the vertex form of the
quadratic function
15. HOMEWORK
Page 199
#9, 15 – 18 all
#27 – 33 odd: Graph each function. Identify the
vertex, axis of symmetry, the maximum or minimum
value, and the domain and range.
#35 – 37all, 41