Name:__________ warm-up 9-4

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Presentation transcript:

Name:__________ warm-up 9-4 Describe how the graph of the function g(x) = x2 – 4 is related to the graph of f(x) = x2. Describe how the graph of the function h(x) = 3x2 is related to the graph of f(x) = x2 Describe how the graph of the function h(x) = 3x2 is related to the graph of f(x) = x2. g(x) = is related to the graph of f(x) = x2

What transformation is needed to obtain the graph of g(x) = x2 + 4 from the graph of f(x) = x2 – 1? Which function has a graph that is the same as the graph of f(x) = 3x2 – 2 shifted 5 units up? A. f(x) = 3x2 – 7 B. f(x) = 3(x – 5)2 – 2 C. f(x) = 3(x + 5)2 – 2 D. f(x) = 3x2 + 3

Details of the Day Activities: EQ: What can a quadratic function graph tell you? I will be able to… * Activities: Warm-up Review homework Notes: Class work/ HW Vocabulary: completing the square Complete the square to write perfect square trinomials. . Solve quadratic equations by completing the square.

9-4 Solving a quadratic by completing the Square Quadratics – completing the square Quadratics – completing the square Quadratics – completing the square Quadratics – completing the square

A Quick Review Describe how the graph of the function g(x) = x2 – 4 is related to the graph of f(x) = x2. Describe how the graph of the function h(x) = 3x2 is related to the graph of f(x) = x2 Describe how the graph of the function h(x) = 3x2 is related to the graph of f(x) = x2. g(x) = is related to the graph of f(x) = x2

A Quick Review What transformation is needed to obtain the graph of g(x) = x2 + 4 from the graph of f(x) = x2 – 1? What transformation is needed to obtain the graph of g(x) = 2x2 from the graph of f(x) = 3x2 Which function has a graph that is the same as the graph of f(x) = 3x2 – 2 shifted 5 units up? A. f(x) = 3x2 – 7 B. f(x) = 3(x – 5)2 – 2 C. f(x) = 3(x + 5)2 – 2 D. f(x) = 3x2 + 3

Notes and examples Find the value of c that makes x2 + 14x + c a perfect square. Solve x2 + 6x + 5 = 12 by completing the square

Notes and examples Solve x2 – 8x + 10 = 30 Solve –2x2 + 36x – 10 = 24 by completing the square. Solve x2 + 8x + 10 = 3 by completing the square.

Notes and examples CANOEING Suppose the rate of flow of an 80-foot-wide river is given by the equation r = –0.01x2 + 0.8x, where r is the rate in miles per hour and x is the distance from the shore in feet. Joacquim does not want to paddle his canoe against a current that is faster than 5 miles per hour. At what distance from the river bank must he paddle in order to avoid a current of 5 miles per hour?

Notes and examples CANOEING Suppose the rate of flow of a 60-foot-wide river is given by the equation r = –0.01x2 + 0.6x, where r is the rate in miles per hour and x is the distance from the shore in feet. Joacquim does not want to paddle his canoe against a current that is faster than 5 miles per hour. At what distance from the river bank must he paddle in order to avoid a current of 5 miles per hour?