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- Quadratic Functions

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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.

5.

Quadratic Functions

5.1

Characteristics of quadratic functions

5.2

Transformations of quadratic functions

5.3

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

5.4

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

5.5

Completing the square

5.6

Converting from general to vertex form by completing the square

5.7

Shortcut: Vertex formula

5.8

Graphing parabolas for given quadratic functions

5.9

Finding the quadratic functions for given parabolas

5.10

Applications of quadratic functions

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Get Started Now5.1

Characteristics of quadratic functions

5.3

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

5.4

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

5.6

Converting from general to vertex form by completing the square

5.7

Shortcut: Vertex formula

5.9

Finding the quadratic functions for given parabolas