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Warm up 1.Factor: x 2 + 6x + 9 2.Factor : 10x 2 + 15x 3.Simplify 4.Simplify:

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Presentation on theme: "Warm up 1.Factor: x 2 + 6x + 9 2.Factor : 10x 2 + 15x 3.Simplify 4.Simplify:"— Presentation transcript:

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2 Warm up 1.Factor: x 2 + 6x Factor : 10x x 3.Simplify 4.Simplify:

3 EOCT Review Is the following function even, odd, or neither? a)evenb) oddc) neither a

4 EOCT Review a)2b) 1/2 c) -1/2d) -2 b

5 EOCT Review a)2yb) 4xy + 2y 2 c) 4xyd) 0 c

6 Lesson Solving Quadratic Equations in Factored Form y = x 2 + 5x + 6 y = (x + 3)(x + 2)

7 Notes - Solving Quadratic Equations in Factored Form If ab = 0, then a = 0 or b = 0 If the product of two factors is zero, then at least one of the factors must be zero. 3 * 0 = 00 * 3 = 00 * 0 = 0

8 Notes - Solving Quadratic Equations in Factored Form (x + 3)(x + 2) = 0

9 Ex. 1: Solve the equation x 2 + x – 6 = 0 STEP 1: Factor x-2= 0 and x+3 = 0 STEP 3: Solve for x. x-2= 0 x = 2 x+3 = 0 x=-3 STEP 4: Check your answers. x 2 + x – 6 = = 0 0 = 0 x 2 + x – 6 = = 0 0 = 0 (x – 2) and (x+3) STEP 2: Set each factor equal to 0.

10 Solve (Find the x-intercepts) 2) x 2 – 2x = 0 3) x 2 – 8x = -12

11 Ex. 4: Solve the equation x 2 – 10x + 25 = 0 STEP 1: Factor x – 5 = 0 and x – 5 = 0 STEP 3: Solve for x. x – 5 = 0 x = 5 x – 5 = 0 x = 5 STEP 4: Check your answers. 0 = 0 (x – 5) and (x – 5) STEP 2: Set each factor equal to 0. Dont write it twice!!!

12 Extension x feet (x-4) feet a)Find an expression for the area. b)If the area is equal to 5 square feet, find x. x 2 – 4x x = 5

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14 Lets look at some examples where x 2 is already by itself.

15 Examples. Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions.

16 Lets look at some examples where x 2 is NOT by itself.

17 We must solve to get x 2 by itself 1 st !

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19 Falling object model When 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:

20 An 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 sides Divide both sides by –16 Take the square root of both sides So, the answer is 1.4 seconds. It is only the positive of the square root b/c you cant have negative seconds!!!!!


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