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Warm upWarm up
1. Factor: x2 + 6x + 9
2. Factor : 10x2 + 15x
3. Simplify
4. Simplify: 5 6 5 6
125
EOCT Review
Is the following function even, odd, or neither?
a) even b) odd c) neither
a
EOCT Review
a) 2 b) 1/2
c) -1/2 d) -2 b
EOCT Review
a) 2y b) 4xy + 2y2
c) 4xy d) 0
c
Lesson 2.5 - Solving Quadratic Equations in Factored Form
y = x2 + 5x + 6 y = (x + 3)(x + 2)
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 = 0 0 * 3 = 0 0 * 0 = 0
Notes - Solving Quadratic Equations in
Factored Form(x + 3)(x + 2) = 0
Ex. 1: Solve the equation x2 + x – 6 = 0STEP 1: Factor
x-2= 0 and x+3 = 0STEP 3: Solve for x.
x-2= 0
x = 2
x+3 = 0
x=-3
STEP 4: Check your answers.x2 + x – 6 = 04 + 2 - 6 = 0
0 = 0
x2 + x – 6 = 09 - 3 - 6 = 0
0 = 0
(x – 2) and (x+3)STEP 2: Set each factor equal to 0.
Solve (Find the x-intercepts)
2) x2 – 2x = 0
3) x2 – 8x = -12
Ex. 4: Solve the equation x2 – 10x + 25 = 0STEP 1: Factor
x – 5 = 0 and x – 5 = 0STEP 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.
Don’t write it twice!!!
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.
x2 – 4x
x = 5
3.6 - Solving a Quadratic Equation by Square Roots
Let’s look at some examples where x2 is already by
itself.
Examples. Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions.
2 21. 4 2. 5x x 42 x
2 5
5
x
x
2x
Let’s look at some examples where
x2 is NOT by itself.
0483 2 xWe must solve to get x2 by
itself 1st!
483 2 x
162 x
4x
96322 xWe must solve to get x2 by
itself 1st!
642 x
8x
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:
sth 216
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.32160 2 t21632 t Subtract 32 from both sides
Divide both sides by –16 22 tTake the square root of both sides
4.12 t So, the answer is 1.4 seconds. It is only the positive of the square root b/c you can’t have negative seconds!!!!!
sth 216
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