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- Quadratic Functions

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Get Started Now- Lesson: 1a11:16
- Lesson: 1b9:27
- Lesson: 1c10:13
- Lesson: 1d6:30
- Lesson: 2a7:46
- Lesson: 2b3:44
- Lesson: 312:53
- Lesson: 411:39

Three properties that are universal to all quadratic functions: 1) The graph of a quadratic function is always a parabola that either opens upward or downward (end behavior); 2) The domain of a quadratic function is all real numbers; and 3) The vertex is the lowest point when the parabola opens upwards; while the vertex is the highest point when the parabola opens downward.

Basic Concepts: Factoring trinomials, Solving quadratic equations using the quadratic formula, Completing the square, Shortcut: Vertex formula

Related Concepts: Even and odd functions, What is a polynomial function?, Characteristics of polynomial graphs

- 1.
**Determining the Characteristics of a Quadratic Function Using Various Methods**Determine the following characteristics of the quadratic function $y = -2x^2 + 4x + 6$:

• Opening of the graph

• $y-$intercept

• $x-$intercept(s)

• Vertex

• Axis of symmetry

• Domain

• Range

• Minimum/Maximum value

a)Using factoringb)Using the quadratic formulac)Using completing the squared)Using the vertex formula - 2.From the graph of the parabola, determine the:

• vertex

• axis of symmetry

• y-intercept

• x-intercepts

• domain

• range

• minimum/maximum value

a)

b)

- 3.Identifying Characteristics of Quadratic function in General Form: $y = ax^2 + bx+c$

$y = 2{x^2} - 12x + 10$ is a quadratic function in general form.

i) Determine:

• y-intercept

• x-intercepts

• vertex

ii) Sketch the graph. - 4.Identifying Characteristics of Quadratic Functions in Vertex Form: $y = a(x-p)^2 + q$

$y = 2{\left( {x - 3} \right)^2} - 8$ is a quadratic function in vertex form.

i) Determine:

• y-intercept

• x-intercepts

• vertex

ii) Sketch the graph.

14.

Quadratic Functions

14.1

Characteristics of quadratic functions

14.2

Transformations of quadratic functions

14.3

Quadratic function in general form: $y = ax^2 + bx+c$

14.4

Quadratic function in vertex form: y = $a(x-p)^2 + q$

14.5

Completing the square

14.6

Converting from general to vertex form by completing the square

14.7

Shortcut: Vertex formula

14.8

Graphing parabolas for given quadratic functions

14.9

Finding the quadratic functions for given parabolas

14.10

Applications of quadratic functions

14.1

Characteristics of quadratic functions

14.3

Quadratic function in general form: $y = ax^2 + bx+c$

14.4

Quadratic function in vertex form: y = $a(x-p)^2 + q$

14.6

Converting from general to vertex form by completing the square

14.7

Shortcut: Vertex formula

14.9

Finding the quadratic functions for given parabolas