Quadratic Functions
Section 2.1
Quadratic A polynomial function of degree “2”
The graph is a parabola
The inverse of a quadratic DNE because it is not a
function
STANDARD FORM:
Helpful when trying to find zeros (factoring, quadratic formula)
VERTEX FORM:
Helpful when describing transformations
Gives location of the vertex (over h,
up/down k)
VERTEX FORM #2:
Helpful when graphing without use of calculator
Vertex = Max/Min point Axis of Symmetry: x = h
(h, k)
Determine the vertex
1.) f(x) = 2(x – 5)2 + 1
2.) f(x) = (x + 2)2 + 1
3.) f(x) = 3x2 + 8
How to find the vertex from standard form
Option #1: Formula
Option #2: Complete the square
Ex. Write the equation in vertex form
f(x) = 5x2 – 6x + 4
Completing the Square Makes it possible to FACTOR
Step 1: Must be in the form x2 + bx
Step 2: Add to the side with “b”
Step 3: Add an equal amount (after distributing) to the other side
Step 4: Factor
Ex. Write the equation in vertex form
f(x) = 3x2 + 12x + 11
You Try! Write the equation in vertex form using your method of choice:
f(x) = x2 – 6x + 12
Ex. Find an Equation
Vertex at (1, 3) and point (0,5)
Slinky Equation
Vertex of slinky data: ______________
Point from slinky data: _______________
What is the best method for writing this equation in vertex form? Why?
f(x) = -2x2 – 7x – 4