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Completing the Square and the Quadratic Formula Objective: To solve quadratic equations by completing the square and using the quadratic formula.

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Presentation on theme: "Completing the Square and the Quadratic Formula Objective: To solve quadratic equations by completing the square and using the quadratic formula."— Presentation transcript:

1 Completing the Square and the Quadratic Formula Objective: To solve quadratic equations by completing the square and using the quadratic formula.

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3 Completing the Square When completing the square, we follow the same technique each time.

4 Completing the Square When completing the square, we follow the same technique each time. 1.Variables on one side, constants on the other.

5 Completing the Square When completing the square, we follow the same technique each time. 1.Variables on one side, constants on the other. 2.Make sure the x 2 is a 1x 2.

6 Completing the Square When completing the square, we follow the same technique each time. 1.Variables on one side, constants on the other. 2.Make sure the x 2 is a 1x 2. 3.Take half of the middle term and square it.

7 Completing the Square When completing the square, we follow the same technique each time. 1.Variables on one side, constants on the other. 2.Make sure the x 2 is a 1x 2. 3.Take half of the middle term and square it. 4.Add that number to both sides.

8 Completing the Square When completing the square, we follow the same technique each time. 1.Variables on one side, constants on the other. 2.Make sure the x 2 is a 1x 2. 3.Take half of the middle term and square it. 4.Add that number to both sides. 5.Solve

9 Completing the Square Solve:

10 Completing the Square Solve: Add eight to both sides.

11 Completing the Square Solve: Add eight to both sides. Take half of 2, square it, and add it to both sides.

12 Completing the Square Solve: Add eight to both sides. Take half of 2, square it, and add it to both sides. Solve.

13 Completing the Square Solve: Add eight to both sides. Take half of 2, square it, and add it to both sides. Solve.

14 You Try Solve

15 You Try Solve

16 You Try Solve

17 Completing the Square Solve:

18 Completing the Square Solve: Subtract 3 from both sides

19 Completing the Square Solve: Subtract 3 from both sides Divide each side by 2

20 Completing the Square Solve: Subtract 3 from both sides Divide each side by 2 Take half of 4, square it, add to both sides

21 Completing the Square Solve: Subtract 3 from both sides Divide each side by 2 Take half of 4, square it, add to both sides Complete the square

22 Completing the Square Solve: Subtract 3 from both sides Divide each side by 2 Take half of 4, square it, add to both sides Complete the square Take the square root and solve.

23 Completing the Square Solve: Subtract 3 from both sides Divide each side by 2 Take half of 4, square it, add to both sides Complete the square Take the square root and solve.

24 You Try Solve

25 You Try Solve

26 You Try Solve

27 Vertex Form After completing the square, the equation is in what we call vertex form since you can find the vertex from the equation.

28 Vertex Form After completing the square, the equation is in what we call vertex form since you can find the vertex from the equation.

29 Example 4

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31 The Quadratic Formula Given a quadratic equation of the form: We can solve it using the quadratic formula:

32 The Quadratic Formula Solve using the quadratic formula.

33 The Quadratic Formula Solve using the quadratic formula. Set the equation equal to zero.

34 The Quadratic Formula Solve using the quadratic formula. Set the equation equal to zero. a=1, b=3, c=-9

35 The Quadratic Formula Solve using the quadratic formula. Set the equation equal to zero. a=1, b=3, c=-9 Use the quadratic equation.

36 The Quadratic Formula Solve using the quadratic formula. Set the equation equal to zero. a=1, b=3, c=-9 Use the quadratic equation.

37 The Quadratic Formula Solve using the quadratic formula. Set the equation equal to zero. a=1, b=3, c=-9 Use the quadratic equation.

38 You Try Solve using the quadratic formula.

39 You Try Solve using the quadratic formula. Set the equation equal to zero. a=1, b=-3, c=-7 Use the quadratic equation.

40 Axis of Symmetry The axis of symmetry for a parabola is the vertical line. This is also the x coordinate of the vertex. Put this back into the equation to find the y coordinate of the vertex.

41 Example 4

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43 You Try Write the equation for the axis of symmetry and the vertex for the following.

44 You Try Write the equation for the axis of symmetry and the vertex for the following.

45 You Try Write the equation for the axis of symmetry and the vertex for the following.

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47

48 Homework Page odd Page odd


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