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

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

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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.

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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.

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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.

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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

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Completing the Square Solve:

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Completing the Square Solve: Add eight to both sides.

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

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

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

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You Try Solve

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You Try Solve

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You Try Solve

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Completing the Square Solve:

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Completing the Square Solve: Subtract 3 from both sides

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

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

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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

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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.

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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.

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You Try Solve

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You Try Solve

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You Try Solve

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

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

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Example 4

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

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The Quadratic Formula Solve using the quadratic formula.

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

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

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

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

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

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You Try Solve using the quadratic formula.

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

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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.

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Example 4

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

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

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

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Homework Page odd Page odd

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