1.1 anatomy of a quadratic function f2012
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1. Anatomy of a Quadratic Function
Unit 1 Quadratic Function
December 10, 2012
Unit 1.Quadratic Functions
Review - Linear Functions
y = mx + b
Ax + By + C = 0
y = 3x - 1
y = -1x 4
1. Anatomy of a Quadratic Function
Unit 1 Quadratic Function
December 10, 2012
**Quadratic - quadratum (Latin) - 'square'
A quadratic function has a degree of 2 instead of 1.
The function always has a x2 in the equation. **
Let's see what it looks like...
f(x) = x2
1. Anatomy of a Quadratic Function
Unit 1 Quadratic Function
December 10, 2012
Anatomy of a parabola
Vertex
Anatomy of a parabola
Axis of Symmetry
1. Anatomy of a Quadratic Function
Unit 1 Quadratic Function
December 10, 2012
Equations for quadratic functions
The most common equation (and the one you need for drawing a parabola) is written in vertex form
f(x) = a(x - p)2 + q
a, p, and q effect the graph in different ways.
y = x2 is the basic graph
The vertex can be found at (p, q)
a makes the parabola wider or narrower.
f(x) = a(x - p)2 + q
a > 0
a < 0
a ≥ 1
a ≤ 1
1. Anatomy of a Quadratic Function
Unit 1 Quadratic Function
December 10, 2012
f(x) = a(x - p)2 + q
q causes a vertical translation.
Easiest to tell when looking at the vertex
f(x) = a(x - p)2 + q
p causes a horizontal translation.
1. Anatomy of a Quadratic Function
Unit 1 Quadratic Function
December 10, 2012
E.g. Draw the parabola using the equation y = -3(x + 4) 2 + 1
1. Anatomy of a Quadratic Function
Unit 1 Quadratic Function
December 10, 2012
E.g. Draw the parabola: y = - 1/4(x - 4)2 + 1
Find the quadratic equation for the following:
1. Anatomy of a Quadratic Function
Unit 1 Quadratic Function
December 10, 2012
E.g. Draw the parabola: y = -(x - 3)2 + 9
Page 157:
#3ab, 4ad
1. Anatomy of a Quadratic Function
Unit 1 Quadratic Function
December 10, 2012
E.g. Determine the quadratic function in vertex form given the graph