Completing the Square

Methods for Solving Quadratics

• Graphing• Factoring• Completing the Square• Quadratic Formula

Square Root Method

Square root method2 64x

Solve: 2 24x

Solve: 2 8 4x

Solve: 2( 3) 32x

Solve: 23( 7) 15x

Solve: 22( 5) 3 25x

Completing the Square

Complete the square to solve.

 

Complete the square to solve.

 

Complete the square to solve.

 

Complete the square to solve.

 

Vertex Form of a Quadratic

• Standard Form:

),(:)(: 2

2

khvertexkhxayformvertex

cbxaxy

Give the Vertex, LOS, and Max/Min

𝑓 (𝑥 )=3 (𝑥−2 )2−4

Give vertex, los, and max/min

𝑦=− (𝑥+3 )2+4

Completing the Square

Used to go from standard form to vertex form or to get the equation in the form of a perfect square to solve Steps:1. Move the constant2. Factor out the # in front of x2

3. Take ½ of middle term and square it4. Write in factored form for the perfect sq.

trinomial5. Add to both sides (multiply by # in front)6. Move constant back to get in (h,k) form

Examplesyxx 1062

Examplesyxx 4162 2

Exampleyxx 2293 2

Exampleyxx 3652 2