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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.

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?

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.

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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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.

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?

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

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

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.

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

Notes and examples

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.

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

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