Completing the Square The Quadratic Formula l u

Completing the Square. The Quadratic Formula. ’l u o ty n r a l le a h W To solve quadratic equations by factoring. To solve quadratic equations by graphing. To solve quadratic equations by completing the square. To rewrite functions by completing then square ry a l u b a c o V Completing the square, quadratic formula, discriminant

Note: Completing the square Completing a perfect square trinomial allows you to factor the completed trinomial as the square of a binomial. You can solve an equation that contains a perfect square by finding square roots. The simplest of this type of equation Problem 1: What is the solution of each equation? A. B.

Your turn What is the solution of each equation? Answers :

Determining Dimensions Problem 2: While designing a house, an architect used windows like the one shown here. What are the dimensions of the window if it has 2766 square inches of glass. Step 1: Find the area of the window Rectangular part is The semicircular is The total amount of glass is Step 2: Solve for x x the length can not be negative so the window is 34 x 68 2 x

Your turn The length of the sides of a rectangular window have the ratio 1. 6 to 1. the area of the window is 2822. 4 sq in. What are the window dimensions. The shorter side is x and the other side is 1. 6 x 1. 6(42)=67. 2 42 x 67. 2 are the dimensions of the window

Solving a Perfect Square Trinomial Equation What is the solution of Perfect square so factor the left side Applied square roots to both sides Rewrite as two equations and solve for x Your turn What is the solution of Answers: 2, 12

Note: You can form a perfect square trinomial form from by adding When solving an equation by completing the square 1. Rewrite the equation in the form To do this, get all terms with the variable on one side of the equation and the constant in the other side. Divide all the terms of the equation by the coefficient of if it is not 1. 2. Complete the square by adding 3. Factor the trinomial 4. Find the square roots 5. Solve for x

Solving by completing the square What is the solution of Rewrite. Get all the terms with x in one side Divide by the coefficient of a=1, b=-4 Find Add 4 to both sides Factor the trinomial Find the square root and solve for x

Your turn 1. What is the solution of Answers: 2. What is in vertex form? Name the vertex and y-intercept. Add to complete the square. Also subtract to leave the function unchanged Factor the perfect square, simplify Vertex: (-2, -10) the y -int. is (0, -6)

Note: You can solve a quadratic equation In more than one way. In general, you can find a Formula that gives values of x in terms of a, b, c The discriminants quadratic equations If If If and the solutions of > 0 two real solutions. Two x-intercepts =0 one real solution. One x-intercept <0 no real solutions. No x-intercepts

Your turn Your school’s jazz band is selling CDs as a fundraiser. The total profit P depends on the amount x that your band charges for each CD. The equation models the profit of the fundraiser. What is the least amount, in dollars, you can charge for a CD to make a profit of $200 a= -1 b= 48 c=-500 the write the Q. F. and Answer: The least amount you can charge substitute for a CD is $15. 29 to make a profit of $200

Your turn again You hit a golf ball into the air from a height of 1 inch above the ground with the initial velocity of 85 ft/sec. The function models the height, in feet of the ball at time t , in seconds. Will the ball reach a height of 115 ft? Now that you know a, b, c use the D. F. The discriminant is negative so the equation Has no real solutions. The golf ball will NOT reach 115 ft

Classwork odd Pg 237 -238 Pg 245 -246 Homework even exercises 12 -75 exercises 11 -55