5Lesson 2.5 - Solving Quadratic Equations in Factored Form y = x2 + 5x + 6 y = (x + 3)(x + 2)
6Notes - Solving Quadratic Equations in Factored Form Zero Product PropertyIf ab = 0, then a = 0 or b = 0If the product of two factors is zero, then at least one of the factors must be zero.3 * 0 = 0 0 * 3 = 0 0 * 0 = 0
7Set each factor equal to zero and solve. Notes - Solving Quadratic Equations in Factored Form (x + 3)(x + 2) = 0Set each factor equal to zero and solve.Check your answers.
8Ex. 1: Solve the equation x2 + x – 6 = 0 (x – 2) and (x+3) STEP 1: Factor(x – 2) and (x+3)STEP 2: Set each factor equal to 0.x-2= 0 and x+3 = 0STEP 3: Solve for x.x-2= 0x+3 = 0x=-3x = 2STEP 4: Check your answers.x2 + x – 6 = 0x2 + x – 6 = 0= 0= 00 = 00 = 0
10(x – 5) and (x – 5) x – 5 = 0 and x – 5 = 0 x – 5 = 0 x – 5 = 0 Ex. 4: Solve the equation x2 – 10x + 25 = 0STEP 1: Factor(x – 5) and (x – 5)STEP 2: Set each factor equal to 0.x – 5 = 0 and x – 5 = 0STEP 3: Solve for x.x – 5 = 0x – 5 = 0Don’t write it twice!!!x = 5x = 5STEP 4: Check your answers.0 = 0
11Extension (x-4) feet x feet x2 – 4x Find an expression for the area. If the area is equal to 5 square feet, find x.x = 5
12We will get x squared by itself. Then we will take the squareroot of both sides of the equal sign.There will be a positiveanswer and a negative answer.
13Let’s look at some examples where x2 is already by itself.
14take the square root of both sides. Examples. Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions.Here, all we have to do istake the square root of both sides.
15Let’s look at some examples where x2 is NOT by itself.
16We must solve to get x2 by itself 1st! add 48divide by 3take the squareroot of both sides
17We must solve to get x2 by itself 1st! subtract 32take the squareroot of both sides
18Falling object modelWhen an object is dropped, the speed with which it falls continues to increase. Ignoring air resistance, its height h can be approximated by the falling object model:
19An engineering student is a contestant in an egg dropping contest. The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking. Find the time it will take for the egg to hit the ground. Disregard air resistance.SOLUTION:The starting height is 32 feet.Now, substitute 0 for h and solve.Subtract 32 from both sidesDivide both sides by –16Take the square root of both sidesSo, the answer is 1.4 seconds. It is only the positive of the square root b/c you can’t have negative seconds!!!!!