Characteristics of quadratic functions

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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; } Common factors of polynomials 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

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