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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. 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. Variables on one side, constants on the other. Make sure the x2 is a 1x2.

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Completing the Square When completing the square, we follow the same technique each time. Variables on one side, constants on the other. Make sure the x2 is a 1x2. 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. Variables on one side, constants on the other. Make sure the x2 is a 1x2. Take half of the middle term and square it. Add that number to both sides.

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Completing the Square When completing the square, we follow the same technique each time. Variables on one side, constants on the other. Make sure the x2 is a 1x2. Take half of the middle term and square it. Add that number to both sides. 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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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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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 304 17-45 odd Page 311 11-33 odd

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Algebra II Honors POD Homework: p. 102 1-11 odds, 13-23 odds (you must use completing the square), and 77, 83 Find all real solutions for the following:

Algebra II Honors POD Homework: p. 102 1-11 odds, 13-23 odds (you must use completing the square), and 77, 83 Find all real solutions for the following:

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