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Still Confused?

Try reviewing these fundamentals first.

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Try reviewing these fundamentals first.

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Get Started Now- Lesson: 1a7:46
- Lesson: 1b3:44
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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.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.

10.

Quadratic Functions

10.1

Characteristics of quadratic functions

10.2

Transformations of quadratic functions

10.3

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

10.4

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

10.5

Completing the square

10.6

Converting from general to vertex form by completing the square

10.7

Shortcut: Vertex formula

10.8

Graphing parabolas for given quadratic functions

10.9

Finding the quadratic functions for given parabolas

10.10

Applications of quadratic functions

We have over 1180 practice questions in Fifth Year Maths for you to master.

Get Started Now10.1

Characteristics of quadratic functions

10.3

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

10.4

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

10.6

Converting from general to vertex form by completing the square

10.7

Shortcut: Vertex formula

10.9

Finding the quadratic functions for given parabolas