Characteristics of quadratic functions

Examples0/10 watched

0/10

Now Playing:Characteristics of quadratic functions– Example 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
1. Using factoring
2. Using the quadratic formula
3. Using completing the square
4. Using the vertex formula
From the graph of the parabola, determine the:
• vertex
• axis of symmetry
• y-intercept
• x-intercepts
• domain
• range
• minimum/maximum value
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.
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.

.body-katex a { word-break: break-word; } Factorise by taking out the greatest common factor Jump to: Notes Prerequisites Related Notes 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. Prerequisites Factoring trinomials Solving quadratic equations using the quadratic formula Completing the square Shortcut: Vertex formula Related Even and odd functions What is a polynomial function? Characteristics of polynomial graphs

No Javascript

It looks like you have javascript disabled.

You can still navigate around the site and check out our free content, but some functionality, such as sign up, will not work.

If you do have javascript enabled there may have been a loading error; try refreshing your browser.