Main Concepts in Lesson:

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AFL's Assigned to Assess

The degree of a quadratic function is 2.

The standard form of a quadratic function is

The graph of a quadratic is called a parabola and has one line of symmetry.

The maximum or minimum point of the graph lies on the vertical line of symmetry.

If “a” is positive the graph opens up and if “a” is negative the graph opens down.

Changing the “c” of the graph affects the parabola’s y-intercept.

Changing “b” also affects the graph.

1.5 Sketch the graph of a quadratic function.

Page 324

Questions #1b, c and e, 2c, e and f

Resources:

Quadratic Graphs http://www.brightstorm.com/math/algebra/quadratic-equations-and-functions/exploring-quadratic-graphs/

Graph Dilations http://www.brightstorm.com/math/algebra/quadratic-equations-and-functions/dilations-of-quadratic-graphs/

Main Concepts in Lesson:

Achievement Indicator:

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If “a” is positive the graph opens up and the vertex of the graph is the point with the least y-coordinate, thus have a minimum value.

If “a” is negative the graph opens down and the vertex of the graph is the point with the greatest y-coordinate, thus have a maximum value.

The vertical line of symmetry is called the axis of symmetry.

The domain is the set of real numbers, (unless the function models a problem that limits the domain) and the range is a subset of real numbers.

1.1 Determine, with or without technology, the coordinates of the vertex of the graph of a quadratic function.

1.4 Determine the domain and range of a quadratic function.

1.5 Sketch the graph of a quadratic function.

1.6 Solve a contextual problem that involves the characteristics of a quadratic function.

Page 333 - 336

Questions #4, 5b and d, 9a and b, 11i and ii, 13 and 16 (Key Question)

Resources:

The Vertex (this movies introduces x = -b/2a for the axis of symmetry)

http://www.brightstorm.com/math/algebra/quadratic-equations-and-functions/the-vertex-and-axis-of-symmetry/

Main Concepts in Lesson:

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When a quadratic function is written in factored form

y = a(x - r)(x - s) each factor can be used to determine a zero of the function by setting each factor equal to zero and solving.

The zeros of a quadratic function correspond to the x-intercepts of the parabola that is defined by the function.

If a parabola has one or two x-intercepts, the equation of the parabola can be written in factored form using the x-intercept(s) and the coordinates of one other point on the parabola.

Quadratic functions without any zeros cannot be written in factored form.

1.1 Determine, with or without technology, the coordinates of the vertex of the graph of a quadratic function.

1.2 Determine the equation of the axis of symmetry of the graph of a quadratic function, given the x-intercepts of the graph.

1.4 Determine the domain and range of a quadratic function.

1.5 Sketch the graph of a quadratic function.

1.6 Solve a contextual problem that involves the characteristics of a quadratic function.

2.1 Determine, with or without technology, the intercepts of the graph of a quadratic function.

2.6 Express a quadratic equation in factored form, given the zeros of the corresponding quadratic function or the x-intercepts of the graph of the function.

Page 346 - 349

Questions #2a and b, 7, 9, 10a, c and d, 11a and c, 12 (Key Question) and 16.

Resources:

Main Concepts in Lesson:

Achievement Indicator:

AFL's Assigned to Assess

A quadratic function that isa 0 written in vertex form,

has the following characteristics:

The vertex of the parabola has the coordinates (h, k).

The equation of the axis of

symmetry of the parabola is

x = h.

The parabola opens upward when a > 0, and the function has a minimum value of k when x = h.

The parabola opens downward when a < 0, and the function has a maximum value of k when x = h.

A parabola may have zero, one, or two x-intercepts, depending on the location of the vertex and the direction in which the parabola opens.

By examining the vertex form of the quadratic function, it is possible to determine the number of zeros, and therefore the number of x-intercepts.

1.1 Determine, with or without technology, the coordinates of the vertex of the graph of a quadratic function.

1.3 Determine the coordinates of the vertex of the graph of a quadratic function, given the equation of the function and the axis of symmetry, and determine if the y-coordinate of the vertex is a maximum or a minimum.

1.4 Determine the domain and range of a quadratic function.

1.5 Sketch the graph of a quadratic function.

1.6 Solve a contextual problem that involves the characteristics of a quadratic function.

2.5 Explain, using examples, why the graph of a quadratic function may have zero, one, or two x-intercepts.

Page 363 - 367

Questions #2d and c, 4, 7, 8, 11b, 12(Key Question) and 15

Resources:

Graph Shifts http://www.brightstorm.com/math/algebra/quadratic-equations-and-functions/vertical-and-horizontal-shifts-of-quadratic-graphs/

Main Concepts in Lesson:

Achievement Indicator:

AFL's Assigned to Assess

When a function is a quadratic function, the maximum/minimum value corresponds to the y-coordinate of the vertex. The algebraic strategy you use to locate the vertex depends on the form of the quadratic function.

All maximum/minimum problems can be solved using graphing technology, if you know the quadratic function that models the situation.

1.3 Determine the coordinates of the vertex of the graph of a quadratic function, given the equation of the function and the axis of symmetry, and determine if the y-coordinate of the vertex is a maximum or a minimum.

1.4 Determine the domain and range of a quadratic function.

1.6 Solve a contextual problem that involves the characteristics of a quadratic function.

Page 377 - 380

Questions # 3c, 6c and d, 7, 11 (Key Question) and 16

Resources: