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Get Started Now- Lesson: 1a7:46
- Lesson: 1b3:44
- Lesson: 212:53
- Lesson: 311:39

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.From the graph of the parabola, determine the:

• vertex

• axis of symmetry

• y-intercept

• x-intercepts

• domain

• range

• minimum/maximum value

a)

b)

- 2.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. - 3.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.

25.

Parabolas

25.1

Introduction to quadratic functions

25.2

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

25.3

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

25.4

Converting from general form to vertex form by completing the square

25.5

Graphing parabolas for given quadratic functions

25.6

Finding the quadratic functions for given parabolas

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