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- Factoring
Characteristics of quadratic functions
- Lesson: 112:53
- Lesson: 1a11:16
- Lesson: 1b9:27
- Lesson: 1c10:13
- Lesson: 1d6:30
- Lesson: 211:39
- Lesson: 2a7:46
- Lesson: 2b3:44
- Lesson: 312:53
- Lesson: 411:39
Characteristics of quadratic functions
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
Lessons
- 1.Determining the Characteristics of a Quadratic Function Using Various Methods
Determine the following characteristics of the quadratic function y=−2x2+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=ax2+bx+c
y=2x2−12x+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(x−3)2−8 is a quadratic function in vertex form.
i) Determine:
• y-intercept
• x-intercepts
• vertex
ii) Sketch the graph.