Solving Quadratic Equations Introduction to completing the square

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Solving Quadratic Equations Introduction to completing the square

Solving Quadratic Equations Introduction to completing the square

Objectives Review: Solve quadratic equations by factoring. Solve equations of the form x 2

Objectives Review: Solve quadratic equations by factoring. Solve equations of the form x 2 = some number. Solve equations of the form (ax + b)2 = some number. Introduce: Solve equations using completing the square.

Factoring l Yesterday, the only way we had for solving quadratics was to factor

Factoring l Yesterday, the only way we had for solving quadratics was to factor or by graphing. Zero-factor property x 2 - 2 x - 15 = 0 (x + 3)(x - 5) = 0 x + 3 = 0 or x - 5 = 0 x = -3 or x = 5 x = {-3, 5} Solution Set

Factoring x 2 = 9 x 2 - 9 = 0 Zero-factor (x +

Factoring x 2 = 9 x 2 - 9 = 0 Zero-factor (x + 3)(x - 3) = 0 property x + 3 = 0 or x - 3 = 0 x = -3 or x = 3 x = {-3, 3} Solution Set

Another Way to Solve Quadratics Square Root Property Recall that we know the solution

Another Way to Solve Quadratics Square Root Property Recall that we know the solution set is x = {-3, 3} When you introduce the radical you must use + and - signs.

Square Root Property of Equations l. If x and b are complex 2 numbers

Square Root Property of Equations l. If x and b are complex 2 numbers and if x = b, then OR

Solve each equation. Write radicals in simplified form. Square Root Property Solution Set

Solve each equation. Write radicals in simplified form. Square Root Property Solution Set

Try this.

Try this.

Solve each equation. Write radicals in simplified form. Square Root Property Radical will not

Solve each equation. Write radicals in simplified form. Square Root Property Radical will not simplify. Solution Set

Try this!

Try this!

Solve each equation. Write radicals in simplified form. Square Root Property Solution Set

Solve each equation. Write radicals in simplified form. Square Root Property Solution Set

Try this?

Try this?

Solve each equation. Write radicals in simplified form. Square Root Property Yikes! A negative

Solve each equation. Write radicals in simplified form. Square Root Property Yikes! A negative inside a radical. Solution Set with imaginary numbers.

Try this…

Try this…

Solve each equation. Write radicals in simplified form.

Solve each equation. Write radicals in simplified form.

TRY THIS

TRY THIS

Solve each equation. Write radicals in simplified form. Notice the solutions are conjugate factors.

Solve each equation. Write radicals in simplified form. Notice the solutions are conjugate factors.

Try This ; )

Try This ; )

Solve each equation. Write radicals in simplified form. Notice that the solutions are conjugates.

Solve each equation. Write radicals in simplified form. Notice that the solutions are conjugates.

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hmmmm

Solving Quadratic Equations by Completing the Square Here is a new way to solve

Solving Quadratic Equations by Completing the Square Here is a new way to solve the same Equation: Remember how to solve Now by factoring: take x 2 1/2 - 2 x - 15 = 0 of x. of the coefficient (x + 3)(x. Square - 5) it. =0 Add the result to both sides. x+3=0 Factor the left. or x. Simplify - 5 = 0 the right. x = -3 or x = 5 Root Property x. Square = {-3, 5}

More practice when a = 1

More practice when a = 1

1. Make the coefficient of the squared term =1. 2. Move all variables to

1. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve. Completing the Square

1. Make the coefficient of the squared term =1. 2. Move all variables to

1. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve. Completing the Square

1. Make the coefficient of the squared term =1. 2. Move all variables to

1. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve.

Completing the Square 1. Make the coefficient of the squared term =1. 2. Move

Completing the Square 1. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve.

Your Task To receive credit for solving quadratic equations by completing the square you

Your Task To receive credit for solving quadratic equations by completing the square you must complete a written assignment. Your teacher will give you the assignment from a resource your school recommends.