Chapter 1 Review
MTH126
1.5 Quadratics
Objectives:
1. Recognize and use the following Forms of Quadratic Functions
Functions:
a) Standard Form
b) Transformation form
2. Identify and calculate the Vertex
Vertex, and interpret the vertex of an application.
3. Find Intercepts,, and interpret in the context of an application.
4. Know and use the Quadratic Formula
Formula.
Quadratics are transformations of 𝑓(𝑥) = 𝑥 .
Standard Form 𝑓(𝑥) = 𝑎𝑥 + 𝑏𝑥 + 𝑐 with vertex −
,𝑓 −
Transformation form (vertex form) 𝑓(𝑥) = 𝑎(𝑥 − ℎ) + 𝑘 with vertex (ℎ, 𝑘)
Write Functions from Graphs
Example: Write an equation of the graph as a transformation of 𝑓(𝑥) = 𝑥 .
Now let’s find the intercepts algebraically and using the calculator
calculator.
(𝑥) = 𝑎𝑥 + 𝑏𝑥 + 𝑐.
The Quadratic Formula gives the horizontal intercepts of the graph of 𝑓(𝑥
𝑥=
±√
Instructor: Lori Jones
CH 1.5 Page 1 of 2
Chapter 1 Review
MTH126
NOTE: If the quadratic formula yields complex numbers (a negative under the square root, so
an imaginary part), then there are no horizontal intercepts.
𝑥=
±√
Application Example: A javelin is thrown in the air where x is the horizontal distance in feet
from the point at which the javelin is thrown. Its height is given by ℎ(𝑥) = − 𝑥 + 8𝑥 + 6.
a) How high is the javelin when it was thrown?
b) What is the maximum height of the javelin?
c) How far from the thrower does the javelin strike the ground?
Instructor: Lori Jones
CH 1.5 Page 2 of 2