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Modeling with Quadratic Functions, Lecture notes of Mathematics

Mathematics

Describe transformations of quadratic functions. Describe transformations of parent functions. Write transformations of quadratic functions. Explore properties of parabolas. Find maximum and minimum values of quadratic functions. Graph quadratic functions using x-intercepts Solve real-life problems. Explore the focus and the directrix of a parabola. Write equations of parabolas. Write equations of quadratic functions using vertices, points, and x intercepts

Typology: Lecture notes

2020/2021

Uploaded on 09/21/2021

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angel-shinez101 🇳🇬

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Clearly, concisely, and completely communicate your mathematical thinking. (1)
Name: Algebra 2 Chapter 2A Review
2.1.1 Describe transformations of quadratic functions.
f(x)=x2
1. Describe the transformation of represented by
g
. Then graph each.
a.g(x)=(x−3)2b.
g(x)=(x−2)2−2c.g(x)=(x+5)2+1
1.1.2 Describe transformations of parent functions.
f(x)=x2
2. Describe the transformation of represented by
g
. Then graph each.
a.g(x)=1
2(
x)2b.g(x)=3(x−1)2c.g(x)= −(x+3)2+2
pf3
pf4
pf5
pf8
pf9
pfa

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Clearly, concisely, and completely communicate your mathematical thinking. (1) Name: Algebra 2 Chapter 2A Review 2.1.1 Describe transformations of quadratic functions. f

x

) = x^2

  1. Describe the transformation of represented by g. Then graph each. a. g

x

x − 3

)^2

b. g

x

x − 2

)^2

− 2 c. g

x

x + 5

)^2 + 1

1.1.2 Describe transformations of parent functions. f

x

) = x^2

  1. Describe the transformation of represented by g. Then graph each. a. g

x

x

)^2

b. g

x

x − 1

)^2

c. g

x

x + 3

)^2 + 2

Clearly, concisely, and completely communicate your mathematical thinking. (1) 2.1.3 Write transformations of quadratic functions. 3a. Let the graph of g be a vertical shrink by a factor of ½ followed by a translation 2 units up f

x

) = x^2.

of the graph of Write a rule (equation) for g and identify the vertex. 3b. Let the graph of g be a translation 4 units left followed by a horizontal shrink by a factor of f

x

) = x^2.

1/3 of the graph of Write a rule (equation) for g.

2.2.2 Find maximum and minimum values of quadratic functions.

  1. Find the minimum or maximum value of these functions. Describe the domain and range of the function, and where the function is increasing and decreasing. a. f

x

) = 4 x^2

  • 16 x − 3 b. h

x

) = − x^2 + 5 x + 9

Clearly, concisely, and completely communicate your mathematical thinking. (1) 2.2.3 Graph quadratic functions using x -intercepts

  1. Graph each function. Label the x- intercepts, vertex, and axis of symmetry. If possible, explain the vertex's coordinates without use of your GDC. a. f

x

x + 1

x + 5

b. g

x

x − 6

x − 2

2.2.4 Solve real-life problems.

  1. The parabola shows the path of your first golf shot, where x is the horizontal distance (in yards) and y is the corresponding height (in yards). The path of your 2nd^ golf shot is a parabola through the origin that reaches a maximum height of 28 yards when x = 45. Compare the distance it travels before it hits the ground with the distance of the first shot. Clearly, concisely, and completely communicate your mathematical thinking. (1) 2.3.1 Explore the focus and the directrix of a parabola.
  2. Use the Distance Formula to write an equation of the parabola with focus F (0, –3) and directrix y = 3.
  1. Write an equation of the parabola with vertex at (0, 0) and the given directrix or focus.

A

directrix: x = − 3

B

focus: F

C

) focus: F 0,^3 ( 2 )

Clearly, concisely, and completely communicate your mathematical thinking. (1) 2.3.3 Solve real-life problems.

  1. Write an equation of a parabola with vertex V (–1, 4) and focus F (–1, 2).
  1. A parabolic microwave antenna is 16 feet in diameter. Write an equation that represents the cross section of the antenna with its vertex at the origin and its focus 10 feet to the right of the vertex. What is the depth of the antenna? 2.4.1 Write equations of quadratic functions using vertices, points, and x intercepts
  2. The graph shows the parabolic path of a performer who is shot from a cannon, where y is the height (in feet) and x is the horizontal distance traveled (in feet). Write an equation of the parabola. The performer lands in a net 90 feet from the cannon. What is the height of the net? If the vertex of the parabola is (50, 37.5), what is the height of the net? Clearly, concisely, and completely communicate your mathematical thinking. (1)
  1. Write an equation of the parabola that passes through the point (2, 5) and has x -intercepts at (–2, 0) and (4, 0). Clearly, concisely, and completely communicate your mathematical thinking. (1)