Warm Up • Write each expression as a trinomial.

• Factor each expression.

21. 5x 2

2. 3 5x

23. 18 81x x 24. 16 24 9x x

2 10 25x x 29 30 25x x

29x 2

4 3x

Quadratics in Vertex Form

Objective: Students will write quadratic equations in vertex form.

Writing a Quadratic Function in Vertex Form

5. Solve for y the equation will be in vertex form.

Steps:1. Write the function in standard form.

2. Set it up to complete the square.

3. Add the square to both sides of the = sign.

4. Write the trinomial as a binomial squared.

Writing a Quadratic Function in Vertex Form

Example 1: Write the function in vertex form and identify its vertex.

2 18 95f x x x

1. Write the function in standard form.2 18 95y x x

2. Set it up to complete the square.

2__ 18 __ 95y x x

Writing a Quadratic Function in Vertex Form

3. Add the square to both sides of the = sign.

281 18 81 95y x x

4. Write the trinomial as a binomial squared.

281 9 95y x

5. Solve for y the equation will be in vertex form.

29 14y x Vertex: 9, 14

Practice: Write a quadratic function in vertex form and identify its vertex.P1: 2 14 11f x x x

27 38y x

2 14 11y x x

2__ 14 __ 11y x x

249 14 49 11y x x

249 7 11y x

7, 38vertex

Practice: Write a quadratic function in vertex form and identify its vertex.

P2: 2 8 10g x x x

24 6y x 4, 6vertex

Writing a Quadratic Function in Vertex Form

Example 2: Factor, write the function in vertex form, and identify its vertex.

22 4 5f x x x 1. Write the function in standard form.

22 4 5y x x

3. Set it up to complete the square.

22 __ 2 2 __ 5y x x

2. Factor the first two terms.

22 2 5y x x

Writing a Quadratic Function in Vertex Form

4. Add the square to both sides of the = sign.

22 1 2 1 5y x x

5. Write the trinomial as a binomial squared.

22 2 1 5y x

6. Solve for y the equation will be in vertex form.

22 1 7y x Vertex: 1, 7

Practice: Write a quadratic function in vertex form and identify its vertex.

P3: 25 50 128f x x x

25 5 3y x 5, 3vertex

Practice: Write a quadratic function in vertex form and identify its vertex.

P4: 23 12 4h x x x

23 2 16y x 2, 16Vertex:

Writing a Quadratic Function in Vertex Form

2 3 16f x x x

1. Write the function in standard form.2 3 16y x x

2. Set it up to complete the square.

2__ 3 __ 16y x x

Example 3: Write the function, using fractions, in vertex form, and identify its vertex.

Writing a Quadratic Function in Vertex Form

3. Add the square to both sides of the = sign.

29 93 16

4 4y x x

4. Write the trinomial as a binomial squared.

29 3

164 2

y x

5. Solve for y the equation will be in vertex form.

23 55

2 4y x

Vertex:3 55

,2 4

Practice: Write a quadratic function in vertex form and identify its vertex.

P5: 22 18 3f x x x

29 75

22 2

y x

9 75,

2 2

Vertex:

Independent PracticeWrite each function in vertex form and

identify its vertex.

21. 24 145f x x x

22. 3 18 7g x x x

23. 2 14 3h x x x