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