Name _______________________
Score _________
Algebra 1B Assignments Chapter 10: Quadratic Functions (All graphs must be drawn on GRAPH PAPER!)
10-3
Pages 567-570: #3-7, 12-17, 22-25, 28-38, 58, 59
10-4
Pages 574-576: #2-6 even, 10-20 even, 21, 24, 26, 28, 31, 34, 50, 52, 56, 57, 60
10-5
Pages 582-584: #4-15, 37, 45, 50, 53, 59-61, 68-70
10-6
Pages 588-589: #1-9, 16-20, 22, 24, 28, 32, 33, 39, 47
Quiz
10-3 to 10-6
Graphing
Worksheet: Solve Quadratics Using a Graphing Calculator
Applications Worksheet: Applications of Quadratic Functions Review
Worksheet: Chapter 10 Review
Test
Chapter 10: Quadratic Functions
Section 10-3 Warm – Up: Simplify each expression. 1.
2. 81
36
Objective:
3.
1 4
4.
49 100
To solve quadratic equations by graphing and using square roots
solutions: values of x that make the equation true (also called x-intercepts, zeros, roots) Example #1: Solve each equation by graphing. a) 2 x
2
2 0
b) 2 x
y
2
0
c) 2 x
y
x
2
2 0 y
x
x
In addition to solving by graphing, you can also solve algebraically using square roots. First isolate the variable, then take the square root. This only works when there is no bx term in the equation y ax
2
bx c .
Example #2: Solve each equation algebraically using square roots. a) 2 x
2
2 0
b) 2 x
2
0
c) 2 x
2
2 0
Example #3: Solve each equation algebraically using square roots. How many solutions does each equation have? a) 4 n
2
3 3
b)
1 2
c
2
8 0
c) 49 y
2
19 3
Example #4: A museum is planning an exhibit that will contain a large globe. The surface area of the globe will be 315 ft2. Find the radius of the sphere producing this surface area. Use the 2
equation S 4 r , where S is the surface area and r is the radius.
Closure Question: How many solutions can a quadratic equation have? How can you determine the number of solutions from the graph?
Section 10-4 Warm – Up: Factor each expression. 1. x
2
3. 2 c
11 x 24
2
2. 3 p
21c 11
4. 4 n
2
32 p 20
2
4 n 15
Objective: To solve quadratic equations by factoring In the previous lesson, you solved quadratic equations by graphing and using square roots. The square root method only works if b 0 . You can solve some quadratic equations when b 0 by using the Zero-Product Property. Zero-Product Property: If ab 0 , then a 0 or b 0 . (If the quadratic is factored, then one of the factors must equal 0.) Example #1: Solve each equation using the Zero-Product Property. a) (2 x 3)( x 4) 0 b) 5 x (6 x 7) 0
To solve quadratic equations by factoring:
Write in standard form ( ax Factor Set each factor equal to 0 Solve each equation for x
2
bx c 0 )
Example #2: Solve x
2
x 42 0 by factoring.
Example #3: Solve 2 x
2
17 x 9 by factoring.
Example #4: Solve 4 x
2
10 x x
2
6 x 21 by factoring.
Example #5: The sides of a square are all increased by 4 inches. The area of the new square is 49 in2. Find the length of a side of the original square.
Closure Question: Explain the process of solving a quadratic equation by factoring.
Section 10-5 Warm – Up: Find each square. 1. ( k 8)
2
2. ( y 11)
2
Factor. 3. x
2
2
10 x 25
4. r
18 r 81
Objective: To solve quadratic equations by completing the square In previous lessons, you solved quadratic equations by graphing, using square roots, and by factoring. A fourth method, completing the square, is another method that can be used to solve quadratic equations. In this class, we will only use the completing the square method if a = 1. Use a generic rectangle and the warm-up problems to see how to find c if you are given b.
Do you see a pattern with b and c? Example #1: Find the value of n such that x
2
12 x n is a perfect square trinomial.
Example #2: Solve x
2
6 x 40 by completing the square.
Example #3: Solve x
2
8 x 29 0 by completing the square.
Example #4: Solve x
2
20 x 32 0 by completing the square.
Closure Question: List the four methods you have learned so far to solve quadratic equations and explain when you would choose to use each method.
Section 10-6 Warm – Up: Evaluate the expression b2 4 ac for the given values. 1. a 7b 8c 1 2. a 1b 3c 4
Evaluate to the nearest hundredth.
2 3 3.
4.
7
12 4
Objective: To solve quadratic equations using the quadratic formula To choose an appropriate method for solving a quadratic equation In previous lessons, you solved quadratic equations by graphing, using square roots, factoring, and completing the square. Unfortunately, not all quadratics can be solved with these methods. A fifth method, the quadratic formula, can be used to solve any quadratic equation. 2
Quadratic Formula:
b b 4 ac
x
( ax
2
bx c 0 )
2a (sing to the tune of “Pop Goes the Weasel”) Example #1: Solve x
2
Example #2: Solve 2 x
5 x 6 0 using the quadratic formula.
2
8 3 x using the quadratic formula.
Example #3: Find the x-intercepts of the graph of y x
2
6 x 3.
Example #4: A child throws a ball upward with an initial velocity of 15 ft/sec from a height of 2 feet. If no one catches the ball, how long will it be in the air? Use the vertical motion formula
h 16 t
2
vt c .
Method Graphing Square Roots Factoring Completing the Square Quadratic Formula
When to Use Use if you have a graphing calculator handy. Use if b = 0. Use if you can factor the equation easily. Use if a = 1, but equation cannot factor easily. Use if the equation cannot be factored easily or at all.
Example #5: Which method would be the best to solve each quadratic equation? Justify your reasoning. a) x
2
b) 2 x c) x
2
d) 6 x
2 x 15 0 2
8 0
3x 7 0 2
5 x 12 0
Closure Question: Write the quadratic formula and say it together as a class.
Solving Quadratic Equations Using a Graphing Calculator Warm – Up: 1. Solve 3 x
2. Solve 2 x
3. Solve x
2
4. Solve 2 x
2
147 0 using square roots.
2
5 x 6 x 40 by factoring.
16 x 31 by completing the square.
2
3 x 7 using the quadratic formula.
Objective: To solve quadratic equations by graphing using a graphing calculator
Example #1: Solve x
2
2 x 8 0 by graphing.
Example #2: Find the x-intercepts of 5 x
Example #3: Find the zeros of 10 x
Example #4: Find the roots of 2 x
2
x 17 2 x by graphing.
2
28 x 46 6 x
2
2
11 x 5 4 x 1 by graphing.
3 by graphing.
Example #5: The Terror Tower launches riders straight up and returns straight down. The equation
h 16t 2 122t models the height h, in feet, of the riders from their starting position after t seconds. Graph the function to determine how long it will take for the riders to return to the bottom.
Example #6: Ricky hits a baseball from a starting height of 3 feet with an initial velocity of 84 ft/sec. Graph the function to determine how long the ball will be in the air if no one touches it. Use the vertical motion formula h 16t 2 vt c .
Closure Question: Explain the difference between solutions, x-intercepts, zeros, and roots of a quadratic equation.
Applications of Quadratic Functions Warm – Up: Solve x
2
4 x 12 using the following methods.
1. Factoring
2. Completing the square
3. Quadratic formula
4. Graphing with a calculator
Objective: To use the vertical motion model h 16t 2 vt c to solve real-world quadratic functions Example #1: A baseball player hits a pitched ball when it is 4 feet above the ground. The initial velocity is 80 ft/sec. How long will it take for the ball to hit the ground? Solve this quadratic equation using two different methods. What is the meaning of the second solution?
Example #2: A basketball player shoots the ball with an initial velocity of 20 ft/sec. The ball is 6 feet above the floor when it leaves her hands. How long will it take for the ball to reach the rim of the basket, 10 feet above the floor? Solve this quadratic equation using two different methods. What is the meaning of the second solution?
Closure Question: Explain which method you prefer to use when solving real-world quadratic functions and why.
