Example 4 Write a Quadratic Function in Vertex Form Write in vertex form. Then identify the vertex. = x 2x 2 10x+22 – y SOLUTION = x 2x 2 10x+22 – y Write original equation. = y?+22x 2x 2 10x+? – () + Prepare to complete the square. = y25+22x 2x 2 10x+25 – () + Add to each side. ()2)2 5 – = – 2 = = y ()2)2 5x – Write as x 2x 2 10x+25 – ()2)2 5x –.

Example 4 Write a Quadratic Function in Vertex Form = y3 ()2)2 5x –– Solve for y. ANSWER The vertex form is. The vertex is. = y3 ()2)2 5x ––– () 3 5,5, You can check your answer by graphing the original equation.

Example 5 Use a Quadratic Equation to Model Area Construction A contractor is building a deck onto the side of a house. The deck will be a rectangle with an area of 1 20 square feet. The contractor has 32 feet of railing to use along 3 sides of the deck. Each side will be at least 8 feet long. What should the length and width of the deck be? SOLUTION – () 322x2xx 120 = length width area = – 322x 22x = Use the distributive property.

Example 5 Use a Quadratic Equation to Model Area – 16xx 2x 2 60 = – 4 = ()2)2 8x – Write left side as the square of a binomial. 2 = 8x – + – Take the square root of each side. x 10 = or 6 Solve for x. Divide each side by 2. – Reject the solution x 6 because the sides of the deck are at least 8 feet long. = – 16xx 2x 2 60 = – Add to each side. = – 2

Example 5 Use a Quadratic Equation to Model Area ANSWER The width is 10 feet. The length is feet. = 322 – 12 () 10

Checkpoint 7. Use Completing the Square Write in vertex form. Then identify the vertex. = x 2x 2 8x8x+19 – y ANSWER = y 3;3; ()2)2 4x – + () 4, Geometry A rectangle has a length of 3x and a width of x 2. The area of the rectangle is 72 square units. Find the length and width of the rectangle. ANSWER 12 units, 6 units