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Name:__________ warm-up 4-7 Find the value of the discriminant for the equation 5x 2 – x – 4 = 0. Describe the number and type of roots for the equation 5x 2 – x – 4 = 0. Find the exact solutions of 5x 2 – x – 4 = 0 by using the Quadratic Formula. Solve x 2 – 9x + 21 = 0 by using the Quadratic Formula.

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The function h(t) = –16t 2 + 70t + 6 models the height h in feet of an arrow shot into the air at time t in seconds. How long, to the nearest tenth, does it take for the arrow to hit the ground?

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Details of the Day EQ: How do quadratic relations model real-world problems and their solutions? Depending on the situation, why is one method for solving a quadratic equation more beneficial than another? How do transformations help you to graph all functions? Why do we need another number set? I will be able to… Activities: Warm-up Review homework – Notes: 4-6 Transformation of Quadratic Graphs Class work/ HW Vocabulary: vertex form. Write a quadratic function in the form y = a(x – h) 2 + k. Transform graphs of quadratic functions of the form y = a(x – h) 2 + k.

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Change of Room Ms. Ogen’s 2 nd Block class should report to Rm 501 on the following dates: Thurs, March 27 Tues, April 1 Thurs, April 3

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Slope SlopeSlopeSlopeSlopeSlopeSlopeSlopeSlope SlopeSlopeSlopeSlopeSlopeSlopeSlopeSlopeSlope https://www.youtube.com/watch?v =7HNccPlXYEg

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A Quick Review Find the value of the discriminant for the equation 5x 2 – x – 4 = 0. Describe the number and type of roots for the equation 5x 2 – x – 4 = 0. Find the exact solutions of 5x 2 – x – 4 = 0 by using the Quadratic Formula. Solve x 2 – 9x + 21 = 0 by using the Quadratic Formula.

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A Quick Review The function h(t) = –16t 2 + 70t + 6 models the height h in feet of an arrow shot into the air at time t in seconds. How long, to the nearest tenth, does it take for the arrow to hit the ground?

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Notes and examples Write y = x 2 – 2x + 4 in vertex form. Notice that x 2 – 2x + 4 is not a perfect square. Write y = x 2 + 6x + 5 in vertex form Balance this addition by subtracting 1 Write y = –3x 2 – 18x + 4 in vertex form

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Notes and examples Which is an equation of the function shown in the graph?

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Notes and examples Read the Test Item You are given a graph of a parabola. You need to find an equation of the parabola. Solve the Test Item The vertex of the parabola is at (2, –3), so h = 2 and k = –3. Since the graph passes through (0, –1), let x = 0 and y = –1. Substitute these values into the vertex form of the equation and solve for a.

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Notes and examples Which is an equation of the function shown in the graph?

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Notes and examples

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Graph y = –2x 2 + 4x + 1. Step 1: Rewrite the equation in vertex form. Step 2The vertex is at (1, 3). The axis of symmetry is x = 1. Because a = –2, the graph opens down and is narrower than the graph of y = –x 2. Step 3Plot additional points to help you complete the graph.

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Notes and examples Graph y = 3x 2 + 12x + 8. A. B. C. D

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