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) ) f(x) = (x + 2) ) f(x) = 3x 2 + 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) = 5x 2 – 6x + 4

Completing the Square  Makes it possible to FACTOR Step 1: Must be in the form x 2 + 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) = 3x x + 11

You Try! Write the equation in vertex form using your method of choice: f(x) = x 2 – 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) = -2x 2 – 7x – 4