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