3.1 quadratic functions in vertex form - wordpress.com · 3.1 quadratic functions in vertex form 1)...
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Section 3.1 Notes.notebook
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3.1 Quadratic Functions in Vertex Form
1) Identify quadratic functions in vertex form.
2) Determine the effect of a, p, and q on the graph of a quadratic function in vertex form where y = a(x p)² + q
3) Analyse and graph quadratic functions using transformations.
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3.1 Quadratic Functions in Vertex Form
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"a" "q" "p"• a > 0, opens up
• a < 0, opens down
• a > 1, narrow
• a < 1, wide
• a = 1, regular
• q > 0, vert. shift up
• q < 0, vert. shift down
• p > 0, horz. shift right
• p < 0, horz. shift left
• a > 0, opens up
• a < 0, opens down
• a > 1, narrow
• a < 1, wide
• a = 1, regular
y = a(x p)2 + q
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Drag the equation to the matching graph
y = x2
y = x2 + 3y = x2 3
y = (x + 3)2y = (x 3)2
y = 3x2Click for answer
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Drag the vertex to the matching graph
(0, 3)Click for answer(3, 0)
(5, 4)(4, 5)
(4, 2)(4, 2)
(2, 4)(2, 4)
(0, 0)(3, 0)
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Drag the vertex to the matching equation
Click for answer
y = (x + 3)2
y = (x 3)2y = (x 5)2 + 4y = (x + 4)2 2
y = 2x2 3y = ¼x2(0, 3) (3, 0)
(5, 4)
(4, 5)
(4, 2)
(4, 2)(2, 4)(2, 4)
(0, 0)
(3, 0)
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Lesson Focus: Sketch Graphs of Quadratic Functions
3.1 Quadratic Functions Vertex Form
3.1 Quadratic Functions Vertex Form
Sketch Graphs of Quadratic Functions in Vertex FormDetermine the following characteristics for each function.• the vertex• the domain and range• the direction of opening• the equation of the axis of symmetryThen, sketch each graph.
a) y = 2(x + 1)2 – 3 b) y = 0.25(x – 4)2 + 1
Example 1:
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Lesson Focus: Sketching Quadratic Functions
3.1 Quadratic Functions Vertex Form
3.1 Quadratic Functions Vertex Form
Your TurnDetermine the following characteristics for each function.• the vertex• the domain and range• the direction of opening• the equations of the axis of symmetryThen, sketch each graph.
a) y = (x – 2)2 – 4 b) y = –3(x + 1)2 + 3
Answer Part a
Answer Part b
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Lesson Focus: Equation of Quadratic Functions
3.1 Quadratic Functions Vertex Form
3.1 Quadratic Functions Vertex Form
Example 2:Determine a Quadratic Function in Vertex Form Given Its Graph
a) • Place in the values of the vertex (P, Q)• Place in the values of x and y from the given point (x, y)• Solve for "a"• Write the equation substituting in "a", "p" and "q"
Instructions
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Lesson Focus: Equation of Quadratic Functions
3.1 Quadratic Functions Vertex Form
3.1 Quadratic Functions Vertex Form
Example 2:Determine a Quadratic Function in Vertex Form Given Its Graph
b)
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Lesson Focus: Equation of Quadratic Functions
3.1 Quadratic Functions Vertex Form
3.1 Quadratic Functions Vertex Form
Your TurnDetermine a quadratic function in vertex form for each graph.
a) b)
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What is an xintercept?
What possibilities exist for xintercepts with regards to quadratic functions?
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Sketch each quadratic function and determine the number of xintercepts for each function.
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Without graphing, determine the number of xintercepts for each quadratic function.
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The deck of the Lions' Gate Bridge in Vancouver is suspended from two main cables attached to the tops of two supporting towers. Between the towers, the main cables take the shape of a parabola as they support the weight of the deck. The towers are 111 m tall relative to the water's surface and are 472 m apart. The lowest point of the cables is approximately 67 m above the water's surface.a) Model the shape of the cables with a quadratic function in vertex form.b) Determine the height above the surface of the water of a point on the cables that is 90 m horizontally from one of the towers. Express your answer to the nearest tenth of a metre.
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The towers are 111 m tall relative to the water's surface and are 472 m apart. The lowest point of the cables is approximately 67 m above the water's surface.b) Determine the height above the surface of the water of a point on the cables that is 90 m horizontally from one of the towers. Express your answer to the nearest tenth of a metre.
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The towers are 111 m tall relative to the water's surface and are 472 m apart. The lowest point of the cables is approximately 67 m above the water's surface.a) Model the shape of the cables with a quadratic function in vertex form.
Section 3.1 Notes.notebook
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April 22, 2015
The towers are 111 m tall relative to the water's surface and are 472 m apart. The lowest point of the cables is approximately 67 m above the water's surface.b) Determine the height above the surface of the water of a point on the cables that is 90 m horizontally from one of the towers. Express your answer to the nearest tenth of a metre.
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Suppose a parabolic archway has a width of 280 cm and a height of 216 cm at its highest point above the floor.a) Write a quadratic function in vertex form that models the shape of this archway.b) Determine the height of the archway at a point that is 50 cm from its outer edge.
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The path of a rocket is described by the function where h(t) is the height of the rocket, in metres, and t is the time, in seconds, after the rocket is fired.
a) What is the maximum height reached by the rocket?
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The path of a rocket is described by the function where h(t) is the height of the rocket, in metres, and t is the time, in seconds, after the rocket is fired.
b) How many seconds after it was fired did the rocket reach this height?
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c) How high above the ground was the rocket when it was fired?
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The vertex of a parabola is (2, 4). One xintercept is 7. What is the other xintercept?
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The xintercepts of a parabola are 5, and 7. What is the equation of the axis of symmetry?
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Pgs: 157161: #’s 1, 2ab, 3bc, 47, 8ab, 915, 20, 21