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Quadratic Equations and Tennis Ball Physics

zarifa avatar
zarifa
9 diapositives · 187 Views · Aug 01, 2014

Solve quadratic equations using the quadratic formula and apply ball drop height equations to real-world scenarios. Find solutions, heights, and interaction with the ground.

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Quadratic Equations and Tennis Ball Physics
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  1. Chapter 9 Review Speed Play

  2. Solve each equation by using the quadratic formula. 3x2– 7x + 4 = 0

  3. Solve each equation by using the quadratic formula. x2– 4x + 6 = 0 The determinant is negative. No Real Solution

  4. A tennis ball is dropped from the top of a tall building. The ball’s height, in meters, t seconds after it is released is h(t) = –4.9t2 + 175. Find h(3) and give a real-world meaning for this value. h(3)=130.9 which is the height of the ball 3 seconds after the ball is dropped b. When is the ball 60 meters above the ground? Give your answer to the nearest hundredth of a second. t=4.84 seconds

  5. Tennis ball continued… A tennis ball is dropped from the top of a tall building. The ball’s height, in meters, t seconds after it is released is h(t) = –4.9t2 + 175. c. When does the ball hit the ground? Give your answer to the nearest hundredth of a second. t=5.98 seconds

  6. Tell whether each statement is true or false. If the statement is false, change the right side to make it true. Give the corrected right side in the same form as the original. For example, if the right side is given in factored form, write the corrected version in factored form. • 1. (x + 2)2 = x2 + 4 • 2. (x – 6)(x – 7) = x2 + 42 • 3. 4(x – 1)2 + 6 = 4x2 – 8x + 10 x x x +2 -1 -6 x2 x2 x2 2x -6x -x x x x False; (x + 2)2 = x2 + 4x +4 -x -7x 2x 42 1 4 -1 +2 -7 False; (x - 6) (x- 7) = x2 - 13x +42 True

  7. Solve the equation x2 – 4x – 2 = 0 by completing the square. Leave your answer in radical form.

  8. Consider the equation. y = (x – 6)(x – 2) a. Find the x-intercepts and the vertex of the graph of the equation. x -4 x2 -4x x • Because of the Zero Product Property either (x - 6) = 0 or (x – 2) = 0, • so x = 6 or 2. • Vertex: (4, -4) • x-coord: y-coord: -4x 16 -4 b. Write the equation in vertex form. c. Write the equation in general form.

  9. Write the equation for this parabola in vertex form. From the points shown you can see that there is no stretch nor shrink (over 1 down 1), but there is a reflection and a translation right 2 and down 1.